MTF Mapper user guide

Frans van den Bergh (fvdbergh#at#gmail#dot#com)

July 3, 2019

Contents

1 What can I do with MTF Mapper? 3

1.1 Annotated images ................................. 3

1.2 MTF surface images ................................ 4

1.3 Lens proﬁle MTF plots ............................... 5

1.4 Proﬁle data sets / Autofocus ﬁne-tuning ..................... 6

1.5 Plots of SFR curves (or MTF curves) ....................... 7

1.6 Checking test chart orientation .......................... 8

1.7 Measure the exact focus position (per colour subset if you want) ....... 9

1.8 Command line version outputs .......................... 10

2 Getting started with the GUI 11

2.1 Main window .................................... 11

2.2 The preferences dialog ............................... 14

3 Supported ﬁle types 18

4 Chart types 19

4.1 Perpendicular chart family ............................. 19

4.1.1 lensgrid ................................... 19

4.1.2 grid ..................................... 20

4.2 45◦chart family .................................. 20

4.2.1 perspective ................................. 21

4.2.2 focus ..................................... 22

4.2.3 mfperspective ................................ 23

5 Additional details on how to use the output types 24

5.1 Lens proﬁle MTF plots ............................... 24

5.2 Proﬁle data sets / Autofocus ﬁne-tuning ..................... 25

5.3 Plots of SFR curves (or MTF curves) ....................... 27

5.4 Checking test chart orientation .......................... 28

5.5 Focus distance-, focus shift-, or LoCA measurement .............. 29

5.5.1 Focus shift measurement .......................... 31

5.5.2 Longitudinal Chromatic aberration measurement ............ 31

5.6 Useful command line outputs ........................... 32

6 Autofocus ﬁne-tuning 34

6.1 The method ..................................... 34

6.2 Caveats and disclaimers .............................. 35

7 Cropped images, or single region-of-interest images 36

8 Lens distortion correction 37

9 Frequently Asked Questions 38

10 Acknowledgements 39

A Tips for printing the test charts 39

B Accuracy assessment 41

C User manuals for individual applications 42

1 What can I do with MTF Mapper?

The MTF mapper package oﬀers a collection of tools to measure Modulation Transfer Func-

tion (MTF) values across edges in images. One popular metric derived from the MTF is

called MTF50, which corresponds to perceived sharpness of edges; this means that the MTF

mapper tools can be used to evaluate camera lens sharpness, as well as autofocus behaviour.

MTF Mapper comes with a variety of test charts which can be printed by an end user.

Some of the output types that it supports requires such MTF Mapper test charts, but for

other output types any suitable test chart can be used, including one of your own design.

An important design goal of MTF Mapper was to automate the process as far as possible,

meaning you no longer have to manually draw rubberband boxes around edges.

Here are some of the things you can do with MTF Mapper:

•Check whether your lens is performing as expected, e.g., whether one side of the lens

is perhaps unacceptably soft;

•Check whether your lens is front-focusing or back-focusing;

•Optimize your camera’s auto-focus micro-adjust (or ﬁne-tuning), or if you have a Sigma

Art lens, MTF Mapper can help you to calibrate focus using the dock;

•Measure how much (if any) focus shift your lens experiences on stopping down;

•Measure longitudinal chromatic aberration;

•Measure and visualize camera system MTF / SFR curves.

To get a more visual idea of what you can do with MTF Mapper, consider the following types

of output you can produce with it:

1.1 Annotated images

In an annotated output image, the MTF50 value of an edge is printed on top of the edge

itself. These annotated images are useful to evaluate the sharpness of your camera across the

entire image, but you want to see the numbers (right part of Figure 1), rather than a plot.

The colour of the annotation text is Cyan if MTF Mapper thinks everything is ﬁne, but will

change to Yellow (edge orientation is close to 45◦, or the edge is shorter than about 25 pixels,

which may result in inaccurate results) and ﬁnally Red (better not to trust these, rather ﬁx

the problem). The text may also read “N/A”, which usually means the edge was either at

an orientation of 0◦or at 90◦. (see Figure 2)

Figure 1: Left: A sample image of a printed MTF Mapper “lensgrid” chart. Right: A close-

up crop of the output produced by MTF Mapper. The Cyan numbers indicate the MTF50

value of each edge in cycles per pixel.

Figure 2: Examples of some of the conditions that aﬀect the colour of the annotation text.

Ideally, all your annotations should be Cyan.

1.2 MTF surface images

Derived from the same input images as used to produce Annotated images, the MTF50 surface

images are a colour representation of your MTF50 values measured across your camera’s

sensor.

Note that MTF Mapper’s output is split into meridional and sagittal plots; the main reason

for this is that most cameras have distinctly diﬀerent performance along the meridional and

sagittal directions. The sagittal MTF50 values are derived from edges that are oriented along

radial lines (with respect to the centre of the image), and the meridional MTF50 values come

from the other edges, that are oriented to be tangential to a circle centred at on the image;

see Figure 4.

Figure 3: Left: A sample image of a printed MTF Mapper “lensgrid” chart. Right: MTF

Mapper’s “grid” output, which is a 3D plot of MTF50 values (as the height) across the image.

Figure 4: Meridional vs Sagittal directions.

1.3 Lens proﬁle MTF plots

MTF Mapper can produce plots that are similar to those produced by lens manufacturers,

which show contrast plotted as a function of distance from the lens centre, at a few selected

spatial resolution choices.

Figure 5: Left: A sample image of a printed MTF Mapper “lensgrid” chart. Right: A lens

MTF proﬁle, showing contrast at 10 lp/mm and 30 lp/mm as a function of distance from

the centre of the lens, for both the meridional and sagittal directions.

Note that MTF Mapper’s lens proﬁle plots cannot exactly reproduce the MTF plots published

by the lens manufacturer, mostly because MTF Mapper measures system MTF, which is a

combination of lens MTF and the camera sensor’s MTF. Also note that some manufacturers

publish theoretical rather than measured MTF. Having said that, the shape of MTF Mapper’s

lens proﬁle plots should be similar to the manufacturer’s plot, but the absolute contrast value

will be somewhat lower.

1.4 Proﬁle data sets / Autofocus ﬁne-tuning

This particular MTF Mapper output is speciﬁcally designed to work with a 45◦test chart,

like MTF Mapper’s “perspective” chart type. The details on using this method to adjust

DSLR autoforcus ﬁne-tuning are discussed in Section 6.

Figure 6: Left: A sample image of a printed MTF Mapper “perspective” chart. Right:

MTF50 values plotted as a function of distance.

The vertical blue line in Figure 6shows the location of the edge used for AF, and the green

curve shows the sharpness in relation to this edge, i.e., we can infer from this plot that the

camera AF has been successfully adjusted in this example.

1.5 Plots of SFR curves (or MTF curves)

Derived from the same input images as used to produce Annotated images, MTF Mapper can

plot the SFR curve (or the MTF curve, if you prefer) of a given edge by interactively selecting

the edge within the GUI by clicking on the Cyan text annotation. By holding shift while

left-clicking on the edge, up to three diﬀerent edges can be selected and plotted together;

you can even select all three images from diﬀerent Annotated image outputs to compare, say,

the same test chart edge across diﬀerent aperture settings of the lens.

Figure 7: Two edges have been selected. One is slightly out of focus, the other sharper,

The pop-up window displays the SFR curves for both of these edges by plotting contrast vs

frequency.

Note that even though the example presented in Figure 7relied on the GUI to perform the

edge selection, the actual SFR data of any edge can readily be extracted using the command

line version of MTF Mapper for batch processing.

1.6 Checking test chart orientation

Most of the MTF Mapper outputs rely on setting up the chart to be perpendicular to the

optical axis of the lens, or put diﬀerently, you want your camera’s sensor to be parallel to

the test chart. If your test chart is not perfectly parallel to the sensor, it might appear that,

say, the right side of your lens appears soft (e.g., it would look a little like the MTF surface

shown in Figure 3). You can only really say that the right side of the lens is in fact soft if

you have conﬁrmed that your set-up is good.

There are many diﬀerent methods of aligning your test chart; the simplest method is to

hold a small mirror ﬂat against the centre of the test chart: if your camera can see itself

looking back, you are close. Another approach is to use the built-in “chart orientation” option

provided by MTF Mapper. This absolutely requires a “lensgrid” style test chart, since MTF

Mapper looks at the circular ﬁducial patterns to measure the chart orientation. Figure 8

shows the output: you ultimately want to bring the yaw and pitch angles down to below 1◦,

the lower the better. We can clearly see that the yaw angle is about 2.68◦to the right, so in

this case it is more likely that the lens is ﬁne (no tilted elements), but rather that the set-up

has to be adjusted slightly.

Figure 8: Sample chart orientation output. As indicated by the 2.68◦yaw angle, this chart

is tilted so that the right side of the chart is sligthly further from the camera compared to

the left side.

1.7 Measure the exact focus position (per colour subset if you want)

MTF Mapper can also measure the exact focus position of your camera. If this sounds odd to

you, you might be onto something. Normally one would expect focus position to be handled

either by the autofocus mechanism, or by the photographer. However, if you have a manual

focus lens and you want to adjust the focus distance to an exact value, perhaps in some

machine vision application, then MTF Mapper can help.

Figure 9: From the “focus” type MTF Mapper chart, mounted at a 45◦degree angle, MTF

Mapper can directly measure the depth-of-ﬁeld curve (which was drawn back onto the test

chart image in green), which also gives you the distance of best focus (blue line).

MTF Mapper can be used to measure focus shift in object space, measuring the exact shift

in millimetres. Figure 9shows MTF Mapper’s Focus position output. The amount of focus

shift on stopping down the lens is measured as the diﬀerence between the two focus position

measurements: one captured with the lens wide-open, and another image with the lens

stopped down without adjusting focus.

We can also measure longitudinal chromatic aberration by processing a single image three

times with MTF Mapper, each time using a diﬀerent R/G/B Bayer channel. Figure 10

demonstrates this by displaying the three output images side-by-side. More information on

the focus output type can be found in Section 5.5.

Figure 10: Example of longitudinal chromatic aberration. The same raw image was processed

by MTF Mapper three times, each time using only the indicated colour subset of the sensor’s

Bayer ﬁlter. Notice how much further back the red channel is focussed, relative to the green

and blue channels.

1.8 Command line version outputs

The bulk of MTF Mapper is implemented as a command-line utility, which makes it suitable

for scripted / batch operation. In fact, the only functionality that is exclusively found in the

GUI is the ability to automatically call dcraw to convert raw camera image formats, and the

ability to produce a plot of a single SFR curve (see Section 1.5).

In addition to producing all the graphical outputs described above, the command-line utility

can create a number of text ﬁles containing useful measurements, e.g., a ﬁle giving the

coordinates of an edge together with its MTF50 value, or a ﬁle giving the coordinates of an

edge together with the full SFR curve data.

2 Getting started with the GUI

2.1 Main window

After launching the GUI, you will be faced with a screen that looks like the one portrayed

in Figure 11.

Figure 11: Screen shot of the MTF mapper gui

The ﬁrst thing you probably want to do is open up a ﬁle (or multiple ﬁles) by choosing

File/Open from the menu bar. That gives you the dialog depicted in Figure 12. Input ﬁles

can be in a variety of image formats, including .tif, .png, .jpg, .pgm, or any raw for-

mat supported by dcraw, including .nef, .cr2, .pef, .arw, .orf, .rw2, .dng, .iiq,

.mos, and maybe more.

You may notice that there are two additional Open options, namely Open single edge image(s),

and Open Focus Position image(s). These two entries are used to open very speciﬁc type of

images, which are discussed in Section 7and Section 5.5 respectively. Unless you are dealing

with these speciﬁc image types, use the plain File/Open option.

I have drawn a red rounded rectangle on top of the screenshot to highlight the output selection

options — these correspond loosely to the subsections of Section 1above. There are several

test charts (see Section 4) used by MTF Mapper, and not all of them will work with all the

output types. Table 1summarizes the combinations that are supposed to work.

Figure 12: The File/Open dialog.

Table 1: Combinations of output types and chart types that should work

Output type Compatible chart types

Annotated image lensgrid, grid, perspective, user deﬁned

Proﬁle perspective

Grid lensgrid, grid, perspective (not recommended), user deﬁned

Lens proﬁle lensgrid, grid (not recommended)

Focus position focus, mfproﬁle

Chart orientation lensgrid, focus (not recommended)

As you can see, the Annotated image output is the most ﬂexible, and will work not only with

most of the MTF Mapper test charts, but also with any user-provided test chart that contains

black rectangles (actually, most convex quadrilaterals) on a lighter background. It should

work with ISO 12233:2014 E-SFR test charts (both standard and enhanced versions), but not

with the older ISO 12233:2000 test charts, nor with DPReview’s test charts. It is possible to

crop out sections of the latter two, which will work with MTF Mapper (see Section 7).

Figure 13: Selecting an output to view.

Ok, back to the ﬁle dialog. After you have selected your input ﬁle (or multiple ﬁles with shift-

click or ctrl-click), and the desired output types, click the Open button to start processing.

You should see some entries appear in the Data set tree-view list after a while. Each entry

that successfully produced output can be expanded by clicking on the symbol to the left of

the entry (the symbol is a triangle in QT5 on Linux). In Figure 13 I expanded the entry of

a ﬁle called crop white and selected the sub-entry called annotated (highligthed by the red

box).

You can see the Annotated image output being shown in the Current output panel; if the

image dimensions exceed the window size, then the initial display scale of the image will be

chosen so that one of the image dimensions ﬁlls the window either horizontally or vertically.

You can drag the image in the output window to pan (while holding down the left mouse

button), or you may choose to use the scroll bars. You may also use the mouse wheel to pan

vertically, or hold down the shift key while scrolling the mouse wheel to pan horizontally. You

can zoom in and out by holding down the control key while scrolling the mouse wheel, but

note that the maximum magniﬁcation factor is 2×. If the image is smaller than the window

size, zooming is disabled. Lastly, you can also zoom by holding down the right mouse button

while moving the mouse up/down, or by clicking with any mouse button on the image to set

the point around which you want to zoom, followed by pressing the “+” or “-” keys on the

keyboard.

At the bottom of the Data set control panel you will see three buttons that can be used to

either clear or save all the results currently displayed in the Data set list.

The last panel of the main window can be found in the bottom-left corner: the Image properties

panel. Most of the ﬁelds are self-explanatory, but I should note that these ﬁelds are populated

purely from the EXIF ﬁelds of your image, if present. In particular, the ‘Focus Distance’

property is that reported by the camera, and is not measured by MTF Mapper.

One last thing to note: the size of the output plots/charts is determined by the size of the

main MTF Mapper window. If you maximize the window before you open/process input

ﬁles, then the plots shouls scale to ﬁll the window, which should help on very high resolution

monitors.

2.2 The preferences dialog

The Settings/Preferences dialog is shown in Figure 14. The ﬁrst panel we encounter (top left)

looks rather familiar; indeed, this Output types panel just a copy of the output types options

encountered in the File/Open dialog. The main diﬀerence is that the output types selected

in the Preferences dialog are saved between MTF Mapper runs, and will be used to ﬁll the

corresponding output type options in the File/Open dialog next time you run MTF Mapper.

Figure 14: The preferences dialog.

The top-right panel, Helpers, is rather uninteresting unless you want to use a custom version

of dcraw. Normally, you can safely ignore this panel.

The middle-left panel, Flags, contains a few optional ﬂags that can be set to alter MTF

Mapper’s behaviour. Brieﬂy,

Linear gamma: This option should be oﬀ by default. Most 8-bit images (e.g., JPEGs) will

be encoded with a particular gamma scheme; you can tick this box if you are certain

that your 8-bit input images are linear.

Autocrop: Automatically trim oﬀ a darker background border around your image before

the actual MTF Mapper processing begins. This is purely a speed optimization that

works well if the image circle of your lens is smaller than your sensor. Which happens

very rarely. Alternatively, if your test chart does not ﬁll the image, and the background

behind your test chart is dark enough, this option may also speed up processing a bit.

If unsure, rather leave it oﬀ.

Line pairs/mm units: This option (oﬀ by default) is used to switch MTF Mapper’s output

units from the native cycles/pixel units to line pairs/mm. Turn this setting on if you

want your ‘Lens proﬁle’ outputs to use the normal conventions, where resolution is

expressed in lp/mm. NB: if you turn on this option, then the ‘Pixel size’ ﬁeld in the

Advanced panel of the Preferences dialog must be set to the correct pixel pitch of your

sensor. If you use my default ‘Pixel size’ of 4.78 micron, you are only going to be happy

with the result if you have a Nikon D7000.

Scale plots to window: As previously mentioned, the varous chart/plot outputs produced

by MTF Mapper will be scaled to ﬁll the main window if this option is turned on (as

it is by default). You can safely leave this on.

The bottom-left panel, ESF construction, is a lot more powerful than its unassuming appear-

ance might lead you to believe. The “Bayer channel” option allows you to control how a

colour image is processed: If the ‘None’ option is selected, then your input image will be

converted to a grayscale image before the main MTF Mapper processing starts. Nothing

(much) will happen if your input image was already a grayscale image. Things get a little

more interesting if your input image is a raw camera format: with ‘None’ selected, your

raw image will be demosaiced with the AHD algorithm implemented in dcraw to produce a

16-bit linear RGB image, which MTF Mapper will then promptly convert to a 16-bit linear

grayscale image. The conventional luminance conversion with a 0.213R + 0.715G + 0.072B

weighting is employed (sRGB D65 illuminant). The implication is that MTF Mapper will

report on the MTF values of the luminance channel of your RGB images if you leave the

Bayer channel option set to ‘None’.

If you choose a diﬀerent “Bayer channel” option (‘red’, ‘green’ or ‘blue’) and your input

image is a raw camera ﬁle, then two things happen:

1. dcraw is instructed to produce un-demosaiced output, i.e., dcraw’s “-d” option, and

2. MTF Mapper will compute MTF values using only the selected Bayer colour subset.

The result of this is that no demosaicing algorithm interferes, meaning that we can measure

the MTF of the lens at the chosen wavelength subset. (Strictly speaking, you would still

have to remove the photosite aperture MTF to really obtain the lens MTF, but you get the

idea.) This approach gives us the most accurate method of measuring eﬀects like longitudinal

chromatic aberration, or any other phenomenon that could cause the demosaicing algorithm

to inadvertently mix the MTFs of the diﬀerent wavelength subsets (e.g., Red, Green, or

Blue). You can read up on this feature of MTF Mapper in a journal paper [4].

NB: Just keep in mind that only 25% of the photosites of the sensor will be red or blue, so

it is prudent to use a longer edge for your MTF analysis. Normally, I would recommend an

edge length of at least 60 to 80 pixels for grayscale images (or the luminance image MTF

Mapper derives from a demosaiced RGB image), but you should increase that (perhaps by

using a larger test chart) to at least 200 pixels for the red and blue Bayer channels.

NB: The default Bayer CFA pattern is RGGB. If your sensor uses a diﬀerent pattern (rather

unlikely) you can add --cfa-pattern bggr (or whatever your pattern is) to the ‘Arguments’

ﬁeld in the Advanced panel of the Prefences dialog. See Appendix Cfor all the supported

CFA patterns.

The second entry in the ESF construction panel, called “ESF model”, is used to select which

algorithm MTF Mapper will use internally to estimate the Edge Spread Function (ESF).

The ‘loess’ algorithm produces more accurate results, but it is slightly slower than the legacy

‘kernel’ algorithm. I would recommend using the ‘loess’ algorithm unless you have a speciﬁc

requirement to produce SFR measurements that are compatible with earlier versions of MTF

Mapper (pre- version 0.7.16). The ‘loess’ algorithm is also recommended if you are using a

“Bayer channel” setting of ‘red’ or ‘blue’, since this algorithm is better at dealing with sparse

image subsets near critical edge orientations — see [5] for details.

The middle-right panel, Lens distortion correction, deals with methods to work around lens

distortion. Although MTF Mapper supports multiple lens distortion correction methods, one

should keep in mind that the impact of lens distortion on slanted-edge MTF measurements is

dependend on the length of the edges. Most MTF Mapper test charts feature relatively small

targets (the black rectangles / trapezoids), so the impact of lens distortion will be relatively

small. Having said that, the default is for MTF Mapper to use a ‘piecewise-quadratic’ to

model each edge, which should compensate for severe lens distortion on very large targets

without any meaningfull loss of accuracy. This method is suitable even when using ﬁsheye

lenses. Section 8covers this topic in more detail.

The bottom-right panel, Advanced, covers a mixed bag of options.

Pixel size: The ‘Pixel size’ ﬁeld is almost self-explanatory; this ﬁeld must be set to your

sensor’s pixel pitch, expressed in micron (micrometre) units. This ﬁeld must be set to

the correct value if the ‘Line pairs/mm units’ option is selected in the Flags panel; if

that ﬂag is disabled, then the value of the ‘Pixel size’ ﬁeld is irrelevant, and will not be

used by MTF Mapper.

Threshold: The most mysterious option in MTF Mapper is the ‘Threshold’ ﬁeld. To un-

derstand what this parameter does, one has to consider how MTF Mapper operates.

The ﬁrst step in MTF Mapper’s processing is to threshold the (grayscale) image so

that the dark targets (e.g., black rectangles) are separated from the lighter background

of the test chart. This thresholding step is locally adaptive, but it is still controlled

by a threshold parameter (between 0.0 and 1.0) to select just how dark an object has

to be relative to its surroundings. The default value of 0.55 should work well for most

properly-exposed images, provided that the test chart ﬁlls most of the image.

But occasionally this will fail. Consider the case where you have set up your test chart

indoors, with the ﬁeld of view adjusted to include the whole test chart, with just a little

bit of the background showing around the chart. If this background scene happens to

include a light source that is much brighter than the white part of the test chart, then

that light source will ‘contaminate’ the nearby part of the test chart, causing MTF

Mapper to not detect the black targets (rectangles) there. In other words, the classic

symptoms would be that only some of the black targets are correctly annotated in the

Annotated image output. The ﬁrst (and best) solution would be to not have a bright

light source in the frame. The other potential solution is to decrease the ‘Threshold’

value until all the black targets are successfully detected. Starting from the default

value of 0.55, drop down to 0.4, 0.3, and maybe down to 0.2 if necessary.

You might wonder why I do not just set the default value to 0.3. Well, you could have

the opposite scenario where you have spurious dark objects in the background that

happen to be rectangular enough for MTF Mapper to detect. The default value of 0.55

is a reasonable balance between these two extremes, and works well enough until it

doesn’t, in which case you can decrease it. Simple enough, right?

MTF-XX: By default, MTF Mapper will calculate MTF50 for most of its outputs, such

as the Annotated image,Grid, and Proﬁle outputs. MTF50 is deﬁned as the resolution

(either in lp/mm, or cycles/pixel) at which the MTF curve ﬁrst reaches a value of 50%

contrast. This option allows you to specify a diﬀerent target contrast value in the range

[10%, 90%], so you can calculate MTF20 or whatever you desire. This aﬀects all MTF

Mapper outputs except the SFR curves and the Lensproﬁle output.

Lensproﬁle lp/mm: By default, MTF Mapper will produce Lensproﬁle plots at resolutions

of 10 lp/mm and 30 lp/mm, corresponding to the popular resolutions chosen by lens

manufacturers. You can override these default resolutions with this setting by specifying

up to three resolution choices in the range [1 lp/mm, 500 lp/mm]. Note that you must

have the ‘Line pairs/mm units’ option checked in the Flags panel for these values to be

used, and the ‘Pixel size’ ﬁeld in the Advanced panel must be set to the correct value.

3D plot z-axis relative scale factor: Old versions of MTF Mapper (0.4.x and earlier)

would plot the Grid output (as illustrated in Figure 3) scaled so that the minimum

MTF50 value would be treated as the zero reference for both the z-axis height of the

3D MTF surface, and the colour scale for both the 3D surface and 2D MTF image.

This has the unintended consequence of magnifying even tiny diﬀerences, should your

lens behave very uniformly across the ﬁeld. It also means that it is hard to compare

two diﬀerent plots, since the MTF50 scale can vary a lot between, say, f/1.4 and f/5.6.

In the 0.5.x MTF Mapper versions, the zero reference was always ﬁxed at, well, zero.

The downside of this approach is that you could not see small deviations in an otherwise

very uniform performance across the ﬁeld.

The solution, as implemented in versions 0.6.x upwards, is to leave the choice to the

user. Setting the ‘z-axis relative scale factor’ slider all the way to the left gives you the

version 0.5.x beviour (zero is 0.0), and setting the slider all the way to the right gives

you version 0.4.x behaviour, like so:

Cache size: MTF Mapper will keep recently viewed images (including any output listed in

the Data set panel) in memory to avoid the delay in re-reading and decoding the images

when you rapidly switch between them. This parameter controls how much memory

(RAM) may be used for storing images; setting this value to 1 MB (the minimum)

eﬀectively disables the cache. Adjust to taste.

Arguments: This ﬁeld gives you the opportunity to pass additional options to the MTF

Mapper command-line tool, thus you can obtain behaviour that is not (currently)

exposed in the Preferences dialog. See the MTF Mapper command-line tool manual

page (in Appendix C) for a comprehensive list of available options. For example, if you

wish to turn oﬀ the Savitzky-Golay ﬁltering that MTF Mapper applies to the computed

SFR curves, you can add the --nosmoothing option to the ‘Arguments’ ﬁeld.

If you ﬁnd yourself using the ‘Arguments’ ﬁeld often, let me know and I can try to

extend the Preferences dialog to include the option you require.

Note that from version 0.7.5 and upwards the contents of this ﬁeld is saved between

MTF Mapper sessions. The contents of the ‘Arguments’ ﬁeld is not sanitized, so it

is possible to input invalid arguments, e.g., --bogus. If you entered such invalid ar-

guments, the call to the MTF Mapper command-line tool will fail, and you will get a

pop-up dialogue that will oﬀer to reset the ‘Arguments’ ﬁeld. My advice is to accept

this oﬀer.

3 Supported ﬁle types

MTF Mapper is able to process a wide variety of image formats. The command line utility

can process at least .tif,.png,.jpg,.ppm,.bmp and .pgm ﬁles, and probably a few more

formats supported by OpenCV.

In addition to these, the MTF Mapper GUI adds support for automatic conversion of raw

image formats using dcraw to perform the conversion. At the time of writing, the GUI will

recognize the following raw ﬁle extensions: .NEF,.CR2,.ARW,.PEF,.IIQ,.MOS,.ORF,.RW2,

and .DNG. If you have a speciﬁc format supported by dcraw that I missed, let me know and

I will add it!

As of version 0.6.15, MTF Mapper understands both ICC colour proﬁles, as well as the two

colour spaces supported by JPEG ﬁles via Exif tags (sRGB and Adobe RGB). The slanted-

edge method that MTF Mapper relies on only works on ‘linear light’ images, meaning that

MTF Mapper will undo any non-linear mapping (sometimes referred to as gamma correction)

associated with the ﬁle format / colour space combination for .tif (TIFF) and .jpg (JPEG)

and .png (PNG) ﬁles. The following list summarizes how MTF Mapper deals with non-linear

images:

1. If you open a raw camera ﬁle with the GUI, then MTF Mapper will use dcraw to

produce a linear 16-bit RGB image. This is the most accurate method. (Note: the

command-line mtf mapper tool does not automatically render raw camera ﬁles — you

have to use dcraw or some other converter)

2. If you open a TIFF ﬁle, a PNG ﬁle, or a JPEG ﬁle (GUI or command-line) with an

embedded ICC proﬁle, then MTF Mapper will convert the image to a linear represen-

tation using the proﬁle’s Tone Reproduction Curve. This applies to both 8-bit and

16-bit TIFF and PNG ﬁles.

3. If you open a JPEG ﬁle with some embedded Exif metadata, then MTF Mapper will

determine (well, guess) whether the JPEG ﬁle is in the sRGB or Adobe RGB colour

space, and apply the appropriate transformation to linearize the image.

4. If your JPEG ﬁle has no Exif tags, or does not contain the Colour Space tag, then

MTF Mapper will assume the ﬁle is encoded in the sRGB colour space.

5. If your image is in any other format (e.g., BMP or PNM), then MTF Mapper will

assume that 8-bit images are encoded in the sRGB colour space (but you can override

this with the -l option), and that 16-bit images are linear.

If you want to play safe, use a TIFF/PNG/JPEG ﬁle with an embedded ICC proﬁle. That

takes care of linearizing the data. What about colour? Well, the slanted-edge algorithm only

operates on grayscale images, or one colour channel at a time. MTF Mapper will transform

an RGB image (after linearizing the values if necessary) to a luminance image, i.e., it performs

a CIE RGB-to-XYZ conversion and keeps the Y channel.

If your image contains an ICC proﬁle, then MTF Mapper will use the embedded RGB-to-XYZ

matrix which (according to the ICC speciﬁcation) is already adapted to a D50 illuminant.

If your image is a JPEG ﬁle, then the D50-adapted matrix for either sRGB or Adobe RGB

will be used, as appropriate. For all other ﬁle types, the D65-adapted sRGB matrix will

be assumed (I am aware of the discrepancy in using the D50-adapted matrix from the ICC

proﬁle if present, but the D65-adapted matrix if no ICC proﬁle is found. I might change

everything to D50 in future).

4 Chart types

MTF Mapper comes with a few custom test chart designs to fully realize its potential. These

charts can be partitioned into the perpendicular and 45◦families. All these charts can be

generated using the mtf generate test chart utility bundled with MTF Mapper. This is

a command-line only tool; see Appendix Cfor a full description of its options. The tool

produces output charts in the SVG vector format, which can be opened and edited with the

Inkscape program (and probably many others).

As an alternative, I keep a .zip ﬁle with a couple of charts already converted to .pdf format

on the MTF Mapper project on SourceForge. Go to https://sourceforge.net/projects/

mtfmapper/files/?source=navbar, and look for a ﬁle called

mtfmapper sample test charts xyz.zip,

where xyz will change whenever I update the archive.

4.1 Perpendicular chart family

These charts are designed to be used so that the test chart is parallel to the camera’s sensor,

or equivalently, that the optical axis of the camera is perpendidicular to the test chart.

4.1.1 lensgrid

This chart type is well-suited to most MTF Mapper output types, including Annotated,Grid,

Lens proﬁle and Chart orientation,but not the Proﬁle output type. The particular shape of

the targets, ranging from trapezoids to squares, are speciﬁcally chosen to ensure that the

edges are either purely radial or tangential in their orientation, provided that the camera is

centered on the chart. Many thanks to Bernard Delley who proposed this type of chart on

the DP Review forums.

A quick word on slanted edge orientation is in order. If you have used Imatest in the

past, or you are familiar with the ISO 12233:2000 standard, then you might wonder about

the validity of MTF Mapper’s test charts containing edges that are clearly not placed at

a 5◦angle. The short version is that extensive testing using both simulated imagery and

captured imagery shows that the slanted edge method works just ﬁne when applied to edges

that are not oriented at 5◦(see [1], but I have also independently performed these tests, e.g.,

http://mtfmapper.blogspot.co.za/2015/06/anisotropy.html).

In addition to the slanted edge targets, the chart also features a number of circular ﬁducial

patterns. These patterns are not used in MTF measurements, but are used when automatic

chart orientation measurement is performed (see Section 1.6). If you plan on using the chart

orientation feature, be sure to print the test chart at the correct size; if you closely compare

the A4 and A3 lensgrid charts (for example), you will notice that the circular ﬁducial codes

are diﬀerent. I also recommend that you print the charts without any ‘ﬁt-to-page’ options.

The accuracy of the chart orientation estimate depends on MTF Mapper being able to trust

that the real-world distance between the circular ﬁducial patterns are correct for a given

chart size.

4.1.2 grid

This chart type is provided for backwards compatibility, but I strongly recommend the use

of the lensgrid chart instead.

4.2 45◦chart family

These charts are designed to be used such that the test chart is oriented at a 45◦angle to

the camera’s optical axis (or sensor, for that matter) in either the pitch or yaw directions.

Actually, there is no reason why these charts cannot be used at some other angle, e.g., 30◦;

rather consider that 45◦is a good starting point if you do not know exactly how much

depth-of-ﬁeld to expect.

4.2.1 perspective

The grandaddy of all MTF Mapper test charts, this chart is intended to be used during

autofocus callibration (see Section 6). As such, Annotated image and Proﬁle (NB: not Lens

proﬁle) are the most useful MTF Mapper output types to use with this chart.

4.2.2 focus

This chart type is intended to be used with the MTF Mapper Focus position output type,

which can only be selected by choosing File/Focus Position image(s) from the File menu in

the GUI. Trying to produce other MTF Mapper output types using this test chart is not

recommended.

4.2.3 mfperspective

This chart type is intended to be used with the MTF Mapper command-line output option

--mf-profile. Trying to produce other MTF Mapper output types using this test chart is

not recommended. At the time of writing, this chart and related output type are considered

experimental, and may potentially change in the future.

5 Additional details on how to use the output types

5.1 Lens proﬁle MTF plots

Section 1.3 brieﬂy introduced this output type. As a ﬁrst step, it is critical to ensure that

the test chart is set-up to be parallel to the image sensor, or equivalently, that the test chart

is perpendicular to the optical axis of the camera. The reason for this strict requirement is

clear when one considers how MTF Mapper derives the Lens proﬁle plots.

First, MTF Mapper assumes that the image centre is positioned to coincide with the test

chart centre (the bow-tie). Next, it averages all the MTF measurements (contrast at a given

spatial frequency) at the same radial distance from the centre of the chart, grouping the

edges into the sagittal / meridional orientations along the way. MTF Mapper also estimates

the spread of the measurements at that radial distance by computing the standard deviation

of the samples. Clearly, if the test chart is tilted badly in the left-to-right direction you will

end up averaging across measurements that are in focus, behind the focal plane, and ahead

of the focal plane. This eﬀect will become more pronounced towards the edges of the test

chart.

(a) Lens proﬁle, no chart tilt

(b) MTF50 surface, no

chart tilt

(d) MTF50 surface, sim-

ulated chart tilt

Figure 15: What happens when my chart is tilted slightly?

Figure 15 illustrates this eﬀect using some simulated imagery. Notice that although the

general shape of the MTF curves have been preserved (the solid and dashed lines in Fig-

ure 15(a) and (c)), we see a massive increase in the observed spread of the measurements

(the red/blue shaded parts). The simulated amount of tilt is perhaps a little excessive, but

it should give you an idea of how to recognize tilt in a Lens proﬁle plot. Without further

information (e.g., performing a chart orientation measurement) it is not really possible to

distinguish from Figure 15(d) whether the chart is tilted (poor set-up), or whether the lens

has a tilted element.

Another important aspect when using MTF Mapper to generate Lens proﬁle plots is to choose

the resolution units you want. By default, MTF Mapper does not know the physical pixel

pitch (size) of your sensor, and this information is not reliably recorded in any EXIF tags.

Thus, if you want to produce a Lens proﬁle plot using the typical 10 lp/mm and 30 lp/mm

spatial resolutions, then you must set the ‘Pixel size’ (in the Advanced panel of the Preferences

dialog) to the correct value, in micron. You must also tick the ‘Line pairs/mm units’ box in

the Flags panel.

Figure 16: You can specify up to three diﬀerent spatial resolutions for Lens proﬁle outputs.

If you want to plot the contrast at a diﬀerent spatial resolution, e.g., 50 lp/mm, then you can

explictly tell MTF Mapper which resolution to use by adding --lp3 50 to the ‘Arguments’

ﬁeld of the Preferences dialog. This will add a third curve for 50 lp/mm to the output. You

can override the default resolutions chosen for the ﬁrst two curves with by entering --lp1

20 --lp2 40 into the ‘Arguments’ ﬁeld. See Figure 16.

5.2 Proﬁle data sets / Autofocus ﬁne-tuning

Using the perspective test chart illustrated in Section 4.2.1, the program will construct a

proﬁle such as the one shown in Figure 17. The chart should be photographed at a 45◦angle,

preferrably at the speciﬁed distance for that chart size. Each chart is optimised for a speciﬁc

viewing distance to counter the eﬀects of perspective distortion, and the chart should be

tilted such that the ‘big end’ of the chart is the one that is further away from the camera.

The large central block in the test chart is called the reference block, and the edge of this

block closest to the centre of the chart is called the reference edge. The MTF50 values

computed across the edges of all the blocks in the image are projected onto the y-axis1of

the image, thus forming a new set of data points of the form (y-value, MTF50 value). This

process is illustrated in Figure 18. The idea is that about half of the chart will be in front

1MTF Mapper will auto-detect the orientation of the image. For ease of discussion, this is called the

y-axis.

0.05

0.1

0.15

0.2

1000 1500 2000 2500 3000 3500 4000

MTF50 (cycles/pixel)

column (pixels)

MTF50 (c/p) raw

MTF50 (c/p) smoothed

Expected focus point

Figure 17: Example of proﬁle generated by MTF mapper.

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

800 1000 1200 1400 1600 1800 2000 2200 2400

Figure 18: How the proﬁle is constructed: MTF50 values are collapsed horizontally onto the

y-axis to form the proﬁle.

of the plane of focus, and the other half behind. If the depth of ﬁeld is suﬃciently shallow,

then the closest and furthest of the small blocks will be noticeably blurry. By projecting

the measured sharpness value (MTF50) of each block along horizontal lines (Figure 18), we

obtain a roughly bell-shaped proﬁle as shown in green on the left. The peak of this curve

corresponds to the plane of focus, and blocks that are further or closer than this plane are

out of focus to some degree. The blue line indicates the position of the reference edge.

A complete proﬁle in its usual orientation is shown in Figure 17. The red dots represent

individual MTF50 measurements, and the green curve is merely a smoothed representation

of the same data.

Generally, Proﬁle mode is only intended to be used to calibrate or evaluate the autofocus

sensor of a DSLR; the details of this process are described in Section 6. The objective is to

adjust the camera so that the blue line (reference edge, or focus position) lines up with the

peak of the green curve / red point cloud. If the blue line is far from the peak, then you are

experiencing either front- or back-focus. If your chart was positioned at a 45◦angle so that

the bottom edge was closer to you, then front focus would mean that the blue line appears

to the left of the peak in the green curve. This depends on the orientation of the camera,

though, so you may want to take a look at the Annotated image (see Section 1.1) to orient

yourself. The trick is to remember that the peak in the green curve (or red point cloud)

corresponds to the actual plane of focus, whereas the blue line corresponds to where MTF

Mapper assumes you have placed the autofocus sensor when you framed the shot.

5.3 Plots of SFR curves (or MTF curves)

Figure 19: Two edges have been selected. One is slightly out of focus, the other sharper.

The pop-up window displays the SFR curves for both of these edges by plotting contrast

vs frequency. The two coloured dots drawn over the selected edges in the annotated image

correspond to the colours used to plot the SFR curves.

A brief description of this output type is given in Section 1.5. The following points should

be noted regarding this output type:

1. Left-clicking on the MTF50 text labels (usually Cyan in colour) of the Annotated image

displayed in the Current output panel of the main MTF mapper will cause a new SFR

curve window to pop up, or will cause the current SFR curve window to be replaced;

2. Holding the shift key while left-clicking on the MTF50 text labels will cause additional

SFR curves to be added to the current SFR curve window. You can select these

additional edges from any of the Annotated image outputs in the Data set list, e.g., you

can select the same edge from two images captured at diﬀerent aperture values, or with

diﬀerent lenses, and directly compare their SFR curves.

You could even process a single raw image three times with diﬀerent Bayer channels

selected, and compare the SFR curves of the three channels using this technique.

If the window already contains three curves, shift-clicking will overwrite the last curve

added to the SFR curve window;

3. MTF Mapper draws coloured dots on the Annotated image output to indicate which

edges are being plotted in the SFR curve window;

4. The SFR curve window supports the display of the full SFR curve, i.e., by adding the

--full-sfr option to the ‘Arguments’ ﬁeld of the Preferences dialog before opening the

input ﬁles for processing, the SFR curve will be displayed up to 2.0 cycles/pixel (the

default is 1.0 cycles/pixel);

5. The ‘Save data’ button of the SFR curve window (see Figure 7) will save the currently

displayed SFR curves to a CSV ﬁle. If multiple curves are displayed, then they will

form additional columns in the output CSV ﬁle;

5.4 Checking test chart orientation

A brief overview of this output type is presented in Section 1.6. A close-up of the output

image is shown in Figure 20. The centre of the printed test chart is deﬁned as the point

where the tips of the two black triangles touch, in the shape that resembles a bow-tie.

After successfully extracting the test chart coordinate information from the circular ﬁducial

patterns, MTF Mapper will visualize the chart origin by drawing an orange ‘compass rose’

on top of the output image.

The second important marker symbol, a red circle with four inwards-pointing triangles, is

drawn at the location of the image sensor centre (see Figure 20). This marker should ideally

be close to the orange compass rose, thus serving as a visual indicator of how well the test

chart was centered in the camera frame, but it does not have to be spot-on.

Figure 20: A close-up of the chart orientation output. This is a crop of Figure 8.

The three Tait-Bryan orientation angles (yaw, pitch and roll) are also rendered in colour on

top of the output image. Each rotation is indicated by a short arc ending in an arrow; this

arrow points in the direction of the observed rotation, so corrections must be applied in the

opposite direction. Aim to reduce all three the angles to below 1◦.

Note that MTF Mapper can only estimate the chart orientation accurately if it knows the

focal ratio of the camera. The focal ratio is simply deﬁned as focal length (in mm) divided

by sensor width (in mm). MTF Mapper will attempt to extract this information from the

EXIF tags in the image, but not all camera hardware will provide the relevant tags. In that

case, it is necessary for the user to provide this information using the --focal-ratio option,

which can be added to the ‘Arguments’ ﬁeld of the Preferences dialog of the GUI.

Keep in mind that the chart orientation measurement is based on the geometrical projection

of the lens, not on MTF or sharpness. In other words, if your camera sensor is tilted with

respect to your lens mount (someone dropped a camera, perhaps), then the chart orientation

measurement provided by MTF Mapper will allow you to orient your camera such that the

sensor is parallel to the test chart. By looking closely at the Grid output, you should be able

to see whether the plane of best focus is still parallel to the test chart — if not, then either

your sensor or lens mount is tilted, or your lens contains a tilted element. Repeating with a

second lens should reveal the truth.

5.5 Focus distance-, focus shift-, or LoCA measurement

A brief description of the Focus position output type can be found in Section 1.7; this section

covers some important details. Note that since MTF Mapper 0.6.20 this output type can

only be produced by opening the ﬁles using File/Open Focus Position image(s), but in older

versions a regular checkbox existed to select this output type.

Figure 21: How to set up the chart relative to the camera.

The focus test chart is intended to be used as illustrated in Figure 21. MTF Mapper measures

the focus position relative to the centre of the chart, meaning that focus should be set (using

manual focus) to the section of the chart indicated in Figure 22. You will notice that there

are some chevron-like patterns down the centre of the chart to facilitate manual focusing;

Live View focussing with magniﬁcation is recommended.

The ﬁrst experiment that you can perform with this MTF Mapper feature is to measure

your own manual-focus accuracy. You capture a number of shots, resetting focus to inﬁnity

beforce re-focusing each time, then use MTF Mapper to measure how close to perfect focus

Figure 22: Focus where the red line shows.

Figure 23: The focus error is the value −24.6 mm printed in Cyan on top of the chart image.

you came in each shot. Figure 23 highlights the focus error that you are looking for: the

diﬀerence between the point of peak sharpness and the intended focus position (the centre

of the chart). You can tabulate these values using your favourite spreadsheet to see how

repeatable your manual focus technique is.

The red circle with the four inwards-pointing triangles that can be seen in Figure 23 is a visual

indication of the centre of the image, and thus the sensor. This marker should perferably

coincide with the centre of the chart (indicated with the orange compass rose); it just makes

things easier if you aim the camera so that the centre of the sensor lines up with the centre

of the test chart, and then you try to place the focus on the centre of the test chart.

So how does this MTF Mapper output type work? Well, the wide black bars that run down

the centre of the chart are used to measure MTF50, but only on the wide edges of the

bars. Because the camera is centered on the chart, these measurements are all in a purely

meridional orientation, and the tilt of the chart ensures that each bar is at a slightly diﬀerent

distance from the camera. Actually, MTF Mapper takes multiple MTF measurements along

each of the long edges of these bars to ensure good depth coverage.

Once all the measurements are collected, MTF Mapper ﬁts a rational polynomial function to

the MTF50 vs distance samples; this is the green curve seen in Figures 23 and 9. This green

curve is a direct visualization of a Depth Of Field (DOF) curve, but using MTF50 as the

sharpness criterion instead of using a circle of confusion. Although MTF Mapper projects

this green curve back onto the image of the test chart, the actual measurements are available

in a true depth scale (distance from camera) in millimetres.

Note that you can use the Focus position output of MTF Mapper with a normal demosaiced

image, i.e., Preferences/‘Bayer channel’ set to ‘None’, with raw images or JPEGs, to per-

form the focus position measurement on the luma component of your image. This should

correspond to your normal visual perception of sharpness in the image.

5.5.1 Focus shift measurement

You can measure the amount of focus shift your lens experiences on stoping down directly in

object space (or the ﬁeld, if you prefer that term). First, use manual focus at your camera’s

focusing aperture (usually the maximum aperture of the lens) to adjust your focus until the

focus error (see Figure 23) is small, say, below 10 mm. Then stop down the lens without

adjusting focus, and capture another shot. The diﬀerence between the focus error of the

wide-open shot and the stopped down shot will give you a direct measurement of the amount

of focus shift. This measurement will most likely depend on the overall distance from your

camera to the test chart, so choose a chart size that will work at the camera-to-chart distance

you intend to use the lens at most often.

If you ﬁnd that the focus shift is so extreme that the focus position moves completely oﬀ the

test chart, then you could try to tilt the test chart further away from parallel to the sensor.

This should increase the depth range spanned by the chart, and hence bring the focus shift

into range. The downside of this would be a slight decrease in depth measurement resolution.

5.5.2 Longitudinal Chromatic aberration measurement

Similarly to the above recipe for measuring focus shift, ﬁrst adjust your manual focus position

until the focus error (see Figure 23) is small. Then use the Preferences/‘Bayer channel’

settings to choose the red, green and blue channels, each time using File/‘Open’ to process

the same raw input image in turn. Figure 24 illustrates the results of such an experiment

where we can clearly see that the red channel focuses far behind the blue and green channels

— this happens to be a Nikkor 50 mm f/1.8 AF-D lens shot at f/2.8.

Figure 24: Example of longitudinal chromatic aberration.

5.6 Useful command line outputs

Although this guide is focused on the features oﬀered by the GUI, it seems like a good place

to document the most useful output oﬀered to command-line users of MTF Mapper. The

option in question is “-q”, which would be invoked as mtf_mapper input.tif out -q. This

output option produces SFR data, MTF50 data, and lens distortion data, distributed over

three output ﬁles:

edge mtf values.txt:Each row of the edge mtf values.txt ﬁle contains six space-separated

columns: block id edge x edge y mtf50 corner x corner y. The block id can safely be

ignored (it depends on the order in which target squares were processed). The pair

(edge x,edge y) denote the pixel coordinates of the centroid of the edge, and mtf50 is

the MTF50 value in cycles per pixel (default), or in lp/mm if the --pixelsize option

was speciﬁed. Lastly, the pair (corner x,corner y) denote the pixel coordinates of the

corner of the target (black square) associated with this edge, and can be safely ignored.

edge sfr values.txt:The format of the edge sfr values.txt ﬁle is similar: each row

starts with ﬁve columns: block id edge x edge y edge angle radial angle, followed by

64 more ﬂoating point values denoting the SFR. The edge angle column denotes the

orientation of the edge relative to the image rows/columns, modulo 45 degrees. This

angle should perferably be at least 2 degrees but less than 44 degrees for best results.

The ﬁfth column, radial angle, is just the angle of the radial line from the image centre

to the edge centroid, thus it can be used to determine whether an edge is in a sagittal

or meridional orientation with respect to the image centre, which is assumed to be

centered on the test chart.

The SFR part (the last 64 values on each line of edge sfr values.txt) represents the

contrast values of the SFR (or MTF, if you prefer) sampled at spatial frequencies of i/64

cycles per pixel for i from 0 to 63 inclusive. You can readily transform these frequencies

to another linear resolution scale, e.g., if your sensor’s pixel pitch is 4.78 micron, then

the frequencies can be scaled so that i/64 ×1000/4.78 gives you a resolution scale in

line pairs per mm.

If you use the --full-sfr option together with -q, the SFR component of each line of

edge sfr values.txt will comprise 128 values (rather than 64), and the corresponding

spatial frequencies are i/64 cycles per pixel for i from 0 to 127 inclusive.

edge line deviation.txt:Each row of the edge line deviation.txt ﬁle contains six space-

separated columns: block id edge x edge y slope rise run. The ﬁrst three, block id edge x

edge y, have the same meaning as in the other ﬁles (e.g., edge mtf values.txt). The

interesting columns are, of course, slope,rise and run. Figure 25 illustrates what these

values mean. The ﬁgure shows the curvature of an actual edge processed by MTF

Mapper; the purple ‘+’ symbols are individual measurements of the edge location (in

the v-axis) along the length of the edge (the u-axis), and are clearly aﬀected by image

noise. It helps to keep the scale of the axes in mind: the rise value is only 0.06 pix-

els, with the run dimension weighing in at 70 pixels. The green parabola represents a

curve ﬁtted to the raw data. As shown in the ﬁgure, the run and rise parameters are

measured on the ﬁtted parabola, rather than the raw data points, to avoid the image

noise. The slope value (and fourth column of edge line deviation.txt) is just the

ratio rise/run.

I have yet to perform a calibration experiments to determine the critical values of the

parameters which would partition edges into curved and not-really-curved categories.

For now, keep in mind that the internal MTF Mapper bin size during ESF construction

is 0.125 pixels, meaning that once the rise parameter exceeds this value, you can be

fairly sure that your edge is curved enough to aﬀect slanted-edge measurements that

do not model edge curvature. Since about version 0.6.10, MTF Mapper will model all

edges as curves by default, so the measurements should be accurate even if the edges

are curved.

run

rise

slope

Figure 25: How edge curvature is measured. Keep in mind that the edge modeled here with

the parabola would look pretty straight in the actual image — it just looks so curved here

because of the high magniﬁcation of the v-axis (rise is only 0.06 pixels).

The only reliable, safe way to compare the output of MTF Mapper between diﬀerent images

captured using the same camera (say, an f/2.8 vs an f/4 image capture) is to use the pixel

coordinates (edge x,edge y) of a measurement from image A to ﬁnd the closest corresponding

measurement from image B, assuming you do not move around the camera too much, or

rotate the chart or something like that (in which case you can use the Monkres assignment

algorithm to calculate the correct pairing). Please do not rely on the order of the rows of the

edge mtf values.txt and edge sfr values.txt ﬁles.

6 Autofocus ﬁne-tuning

6.1 The method

The following steps can be used to calibrate the autofocus ﬁne-tuning of a DSLR:

1. Figure 26 illustrates the basic set-up. The distance dis the “distance to chart”, and

the angle θis the “angle with respect to the test chart”.

2. Print out the test chart at a large enough scale. Ideally, your test chart must be

large enough so that you can use it at a distance of 30×the focal length of your lens.

Appendix Aoﬀers some advice on printing your test charts.

Position your camera so that you see the chart from an angle of at least 45◦— the

idea is that you want some of the small blocks to be in front of the plane of focus, and

some of the blocks behind the plane of focus; this is easier to achieve at angles of 45◦

and smaller. The reference edge (Section 5.2) should be exactly at the plane of focus,

but since you are reading this, I take it you are still trying to adjust the autofocus

ﬁne-tuning to achieve this.

Camera

Wall

Test chart

Figure 26: Illustration showing the top view of the autofocus calibration set-up

Figure 27: Where to place your autofocus sensor

3. You must use a tripod, and it is recommended that you use a remote shutter release

or a timed shutter release to minimise vibrations.

4. You should have enough light for an exposure value of 10–11 (for example, ISO 100

F/1.8 at 1/320 s), which translates into about 2500–5000 lux. This amount of light is

required to achieve consistent performance from the AF sensor. I use indirect sunlight

to reach these levels.

5. Set your camera to AF-S (single-servo AF). Select a single AF point — the centre AF

sensor is recommended. This is critical, as any other AF mode / sensor selection will

not produce the desired results. On Nikon bodies, I like to use the AF-ON mode so that

the camera only focuses when I ask it to. For adjusting your AF ﬁne tuning settings,

you should use a single AF operation, i.e., press and hold the AF-ON button until focus

lock is achieved, then release the button. Do not focus a second time.

6. Aim the AF sensor reticule so that it straddles the reference edge (see Figure 27).

Take care that the autofocus sensor is suﬃciently far away from other edges (e.g., the

horizontal edges of the reference block in Figure 27, or any of the small blocks). Keep

in mind that the actual sensing area of the autofocus sensor is typically larger than the

reticule you see in the viewﬁnder, so leave some padding.

7. Manually set the focus of your lens to the near limit, or to inﬁnity.

8. Initiate one AF operation.

9. Capture a shot of the test chart. Lower ISO values are better, since MTF measurements

are more variable if you have a lot of noise.

10. Feed the captured image through MTF mapper to produce a proﬁle (such as illustrated

in Figure 17. The vertical blue line denotes the position of the autofocus reference edge

(at least, the one you should have been using to focus . . . ). The green curve (or red

points) records the MTF50 values measured along the long axis of the image. Since the

test chart was at a 45◦angle with respect to the lens axis, the long axis of the image

is a measure of the distance from the camera. MTF50 values measured at diﬀerent x-

values (in the Figure 17) thus indicate the sharpness, or degree of focus, at that speciﬁc

distance from the camera. The peak of the green curve represents the plane of focus

— the objective is to line up the peak of the green curve with the blue vertical line.

11. This procedure (steps 7–10) should now be repeated at various autofocus ﬁne-tuning

settings on your camera. You should be able to see the peak of the green curve shift

left or right as you adjust this value. I recommend capturing your images in batches,

ﬁrst stepping your autofocus ﬁne-tuning through the range in large steps, running the

images through MTF mapper, and then repeating this in the optimal range with smaller

steps until you are satisﬁed that you have calibrated your autofocus ﬁne-tuning to the

desired level of accuracy.

6.2 Caveats and disclaimers

Please note that this procedure of calibrating autofocus ﬁne-tuning on your DSLR is based

on some of my own assumptions, which have not been tested rigorously before the release of

this software. Here follows some background; you are most welcome to skip this section.

Phase-detection autofocus in DSLR cameras works by collecting light from opposite sides of

the lens (the aperture, really), if the article on Wikipedia is accurate2. These two beams of

light are steered to two independent linear sensors — I suspect that they are simply small

strip-like CMOS sensors nowadays. Using cross-correlation, the AF module then measures

2http://en.wikipedia.org/wiki/Autofocus

the phase shift between the data collected from the two linear sensors; this phase shift will

directly correspond to the degree of defocus. With this information, the AF module can then

drive the AF motor by approximately the correct amount to eliminate the phase diﬀerence

between the signal received by the two linear sensors, which should bring the object under

the relevant AF sensor into focus.

So the real question is: what algorithms do the AF modules really use to measure the phase

shift? Well, I currently do not know. If you design AF modules, please ﬁll me in, and I

can update my test charts to agree more closely with what the AF modules expect to see.

Many AF test charts are available on the Internet, however, most of them use thick line

(bar-shaped) target to draw the AF sensor’s attention. Someone on the Internet (now, there

is a reference you can count on) pointed out that bar targets are a poor choice, because they

may be too thin for the AF sensor to detect. I found this argument appealing, because the

AF sensor must have limited resolution. There is an additional problem with a bar target:

which edge of the bar target is the AF module going to focus on? And this process led me

to the design of my own test charts. Rather than using a bar as an AF target, why not

use a step edge? If the AF module really does use cross-correlation to measure the phase

diﬀerence, then a step edge would produce the best possible results. There would also be

no ambiguity as to where the sensor is focusing, since the step edge only has one feature to

focus on.

Well, it seems to work. At least for my camera bodies and lenses.

I also found it annoying to have to use visual inspection to determine whether I have set

the autofocus ﬁne-tuning optimally. Visual inspection certainly is a quick way to evaluate

the results in the ﬁeld, but I want to see some objective data. I want to know that I have

calibrated my lenses perfectly. Anyhow, if you have made it this far, you probably understand.

MTF50 is certainly not the ﬁnal word on image acuity (read the excellent Zeiss papers for a

start), but it does provide a reasonable relative measure for the autofocus calibration problem.

The MTF50 estimates extracted by MTF Mapper are reasonably accurate (see Appendix B),

at least as far as internal consistency goes with my own edge image generator. You should

be able to obtain repeatable results within a 5% relative margin.

Lastly, you should know one very important thing about autofocus systems: they are not

perfect. The tolerances of the AF system (AF module, lens drive accuracy, etc.) are such

that they strike a balance between speed and accuracy.

With MTF mapper, you can empirically observe this eﬀect: manually set focus to inﬁnity,

switch to AF, capture image. Now select near focus (manually), switch to AF, capture

image. Comparing the proﬁle plots of produce by MTF mapper you should be able to see

which image was captured from which direction, and the distance between the peaks in the

proﬁles should roughly correspond to this “zone of acceptable focus” for that subject distance

and magniﬁcation.

7 Cropped images, or single region-of-interest images

Occasionally it is not possible to use an MTF Mapper test chart. This could be because a

review site only uses an older ISO 12233:2000 test chart, or because you are using a back-lit

razor blade (the ultimate DIY reference edge if you do not have an optics lab). Unfortunately

MTF Mapper cannot automatically isolate the edge of interest in such images, however, it is

still possible to use MTF Mapper to analyze cropped regions of such images.

Figure 28 shows one example of such a cropped image of a slanted edge. To use such an image

with MTF Mapper, just pass the --single-roi option to the command-line tool, or open

your ﬁles using the File/Open single edge images(s) GUI option. Of course, the only sensible

visual output for such an input image would be the Annotated image option; from there you

can view the SFR curve in the gui. (Or see the -q output option for the command-line tool).

(a) Input im-

age

(b) Annotated

image

Figure 28: Single ROI example

The edge can be in either a vertical or horizontal orientation, and it does not matter on

which side of the image the dark side of the edge appears.

8 Lens distortion correction

Lens distortion can have a fairly signiﬁcant impact on slanted-edge MTF measurements. If

a slanted edge in the captured image is no longer straight, but rather curved, the measured

MTF will decrease. The magnitude of the impact of lens distortion on MTF measurements

is highly dependent on the length of the edge relative to the magnitude of the distortion. If

the edge is short enough, or the distortion is weak enough, then you can get away without

explicitly correcting for distortion. For the other cases, there are several strategies to deal

with lens distortion:

Undistortion using an ideal lens model: Use a pre-deﬁned lens model to “straighten”

the edges before applying the slanted edge method. This option is appealing if you

are dealing with a ﬁsheye lens, and you wanted to undistort the image anyway. A

modiﬁed version of the slanted-edge method is required to make this work; you cannot

simply undistort the image before passing it to MTF Mapper, since this will produce

unrealistically low measurements in areas with large compression, such as the corners

of a ﬁsheye lens.

MTF Mapper oﬀers support for this type of lens distortion correction through the

‘Equiangular’ and ‘Stereographic’ options under the Lens distortion correction panel

of the Preferences dialog. For both these models it is compulsory to specify the focal

length of the lens in the ﬁeld provided. In addition, the ‘Pixel size’ ﬁeld in the Advanced

panel must also be set to the correct value (sensor photosite pitch, in micron), and the

‘Line pairs/mm units’ option must be enabled in the Flags panel.

Lastly, keep in mind that the two supported lens models do not allow for any additional

deviation from the ideal equiangular or stereographic ﬁsheye lenses.

Undistortion using a ﬁtted model: Fit a parametric lens distortion model to “straigthen”

the edges, using the image of the test chart itself to estimate the distortion parameters.

Think of it as an automatic lens undistortion model; once these model parameters have

been estimated the internal implementation is basically the same as for the ﬁsheye

undistortion models. In my limited testing, this automatic lens undistortion feature

worked just ﬁne when applied to ﬁsheye lens images, although I did not test circular

ﬁsheye lenses.

MTF Mapper supports this approach through the ‘radial’ option under the Lens dis-

tortion correction panel of the Preferences dialog. There is no requirement to specify a

pixel size, or focal length, or to enable the ‘Line pairs/mm units’ option.

The main disadvantage of this approach is that it is inherently a two-pass scheme, thus

it will be noticebly slower than other undistortion options.

Direct modeling of curved edges: Treat each edge in the image independently as a curve,

rather than a straight line. This requires a modiﬁed implementation of the slanted-edge

algorithm, but other than requiring a model-ﬁtting step to approximate each edge, rel-

atively little extra work has to be performed, making this approach almost transparent

in terms of cost. This method has the distinct advantage of not requiring a lens model,

and not requiring an undistorted image to be produced. The usual approach is to

ﬁt a quadratic polynomial (i.e., a parabola) through the curved edge; this is a pretty

good approximation for most types of lens distortion, excluding ‘moustache’ distortion.

If you have to deal with ‘moustache’ distortion a piecewise-quadratic polynomial ﬁts

much better.

MTF Mapper now uses the piecewise-quadratic curved edge approach to dealing with

lens distortion by default. You can try the garden-variety quadratic curved edge model

by selecting the ‘quadratic’ option under the Lens distortion correction panel of the

Preferences dialog. If you want to revert to a plain-vanilla straight edge model, choose

the ‘none’ option.

9 Frequently Asked Questions

1. Your program gave me a value of xcycles per pixel. Is this any good? Answer: Ac-

cording to Norman Koren (http://www.imatest.com/guides/modules/sfr), a value

of 0.33 cycles per pixel is pretty good for unsharpened raw images (emphasis mine).

This is somewhat misleading, though, since expressing MTF50 as c/p is not indepen-

dent of the sensor resolution, and Norman may have been referring to an 8 MP sensor.

Take, for example, a sample of the Nikkor 35 mm f/1.8 prime lens on a D40 body. This

combination achieves MTF50 values of around 0.28 c/p. The same lens on a D7000

body achieves around 0.22 c/p. If these values are expressed as line pairs per millimetre

(lp/mm), we actually see 36 lp/mm on the D40, and 46 lp/mm on the D7000. In this

case, it means that the lens is actually able to resolve more detail than what the D40

could capture. This also explains why I suddenly thought the lens looked softer on

the D7000 — the per-pixel sharpness was deﬁnitely lower, even though the eﬀective

sharpness was higher.

So while c/p units are convenient because they do not require knowledge of the pixel

(or sensor) size, they are not portable to other sensors for the very same reason. I prefer

to use lp/mm when comparing lenses, but c/p are more natural for synthetic images.

2. Cycles per pixel? I wanted lw/ph or lp/mm! Answer: Support has been added for

lp/mm by specifying a pixel size with the --pixelsize option. You can also convert

manually using the following relationship:

MTF50lp/mm =MTF50c/p×hpixels

hmm

(1)

MTF50lw/ph = 2 ×MTF50c/p×hpixels (2)

where hmm is the image height in mm, and hpixels is the image height in pixels.

10 Acknowledgements

Although I am the sole author of MTF Mapper, quite a few of the ideas that have gone

into MTF Mapper were contributed by users, or their request for features motivated me to

implement said functionality. I extend thanks to the following entities:

•Jack Hogan

•Ed Dozier

•craig66 (of DP Review forums)

•Jim Kasson

•Bernard Delley

•Alpa, who funded the development of the Focus position functionality

•Brandon Dube

A Tips for printing the test charts

I have printed the MTF Mapper test charts using a variety of printers, and have the following

advice to oﬀer:

•If you are printing on paper, you should aim to use the thickest paper available. Some-

thing like 120 g/m2is probably the bare minimum. All my charts printed on standard

80 g/m2paper warped horrendously with changes in humidity.

•The test charts work best when they are quite ﬂat. I have worked with an A0 print of

the perspective chart that was simply taped to a plastered wall, and everything seemed

to be ﬁne. If, on the other hand, you are using the grid chart to look for MTF variations

in the focal plane, then it is critical to keep the chart perfectly ﬂat. I have found that

foam board works very well, especially if you use a spray glue to ﬁx the printed chart

to the foam board.

•Even spray glue combined with a foam board is not good enough to prevent thin paper

from warping due to changes in humidity. If you plan on using a chart more than

once, you must use thick paper. It might also help if you use mechanical clamps (e.g.,

Bulldog clips) in stead of spray glue to fasten your chart to the backing.

•I have yet to try this myself, but a local printer can print on a self-adhesive vinyl sheet.

This should be immune to humidity, but obviously this will be much more expensive

than printing on plain paper.

•Another untested idea is to use a laser-marking (laser-engraving) machine to “print”

onto a painted aluminium sheet. Let me know if you’ve tried this!

•Print quality is probably not critical when using the perspective charts — I have used

badly printed (streaky, not quite solid) charts, and that seemed to be OK on an A0

scale.

•Print the largest chart you possibly can for a given focal length. In practice, I have

found that the A0-size charts work very well for lenses shorter than 50 mm, since they

allow me to keep the chart at a realistic distance. I have yet to perform extensive tests

on A4 charts, but I suspect they are only safe to use with longer focal lengths (e.g., 200

mm or longer). Furthermore, at greater distances, you can get away with lower quality

prints — 300 DPI prints are ﬁne on an A0 chart, but may become a problem on A4

charts.

•Test chart quality is critical if you want to obtain absolute results, such as when you

want to compare your results to other sources (online, etc.). If you are just evaluating

the relative performance of two lenses, e.g., two copies of the same lens, or two diﬀerent

brands of 50 mm prime lenses, then you can get away with a lower quality test chart.

B Accuracy assessment

The evaluation of the accuracy of an implementation of the slanted-edge method can become

rather complicated. The MTF Mapper blog (https://mtfmapper.blogspot.com) contains

quite a few articles on this topic. For now, I will just include one graph illustrating the

accuracy of MTF Mapper compared to two other popular implementations: Imatest and

Quick MTF. The test involves generating a large number of test images containing slanted

edges, repeating the rendering of each image with a diﬀerent simulated (expected) MTF50

value, in the presence of a low (but realistic) level of image noise. Afterwards, the three

contenders were used to measure the MTF50 value of the simulated edges. I choose to use

the relative error, meaning that the error is expressed as

errrelative = 100 ·MTF50measured −MTF50expected

MTF50expected

since this makes the range of errors comparable across diﬀerent expected MTF50 values (or

otherwise the blurry edges appear to have almost no error relative to sharp edges).

Figure 29: Accuracy comparison: MTF Mapper vs. Imatest vs. Quick MTF

At any rate, over the multiple samples at each simulated MTF50 value, the 95th percentile of

|errrelative|was computed; the results are presented graphically in Figure 29. To interpret this

graph: 95% of the 240 edges with an expected MTF50 of 0.25 cycles/pixel were measured

with MTF Mapper to have an estimated MTF50 value between about 0.245 and 0.255, i.e.,

the measurements were within 2% (roughly the height of the red bar at 0.25 cycles/pixel on

the x-axis).

Under these conditions MTF Mapper is at least as accurate as Imatest 4.1.12, and deﬁnitely

more accurate than Quick MTF. Informal experiments with the slanted-edge plugin for Im-

ageJ as well as Mitre SFR indicate that those implementations are signiﬁcantly less accurate

than MTF Mapper.

C User manuals for individual applications

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1. MTF_MAPPER

1 mtf_mapper

mtf_mapper — compute MTF50 edge sharpness measure in images

Synopsis

mtf_mapper [OPTIONS]INPUT_IMAGE OUTPUT_DIR

DESCRIPTION

mtf_mapper computes the edge acuity (sharpness) of slanted edges in images. It automatically detects dark rectangular objects

on light backgrounds, and computes the MTF50 values across each of the edges. Output takes several forms (see -p,-s,-a

and -q output options). To test mtf_mapper, images with rectangles containing known MTF50 values can be generated with

mtf_generate_rectangle.

OPTIONS

-t threshold, --threshold threshold

Specify the dark object threshold, with a default of 0.55. Lower values are required if your dark objects are light relative

to the background, e.g., gray rectangles rather than black rectangles. You can try lower values, e.g., 0.3 or even 0.2 if MTF

Mapper does not appear to detect any dark objects.

--threshold-window fraction

Specify the fraction of the smaller image dimension (height or width) that will be used as a window size during automatic

thresholding to detect dark objects (see -t). The default of 0.3333 works well when the test chart has a white background.

If your dark targets tend to have some other chart feature surrounding them (think QA-62 Scanner targets) then you can

try to reduce this fraction; choosing the fraction to be roughly equal to the size of the dark target (as a fraction of image

height) should work.

-l, --linear

Linear input mode; assumes that an 8-bit input image has a linear intensity scale. The default is to assume that 8-bit input

images have an sRGB gamma intensity proﬁle (approximately gamma 2.2).

--pixelsize size

Specify the sensor’s pixel size (pitch) in microns. This option implicitly switches the MTF50 output units (for some output

types) to line pairs per mm, or lp/mm (the default is cycles per pixel, or c/p).

--bayer red|green|blue|none

Process only the speciﬁed Bayer sites. This option can be used to bypass the effects of Bayer demosaicing interpolation

when suitable raw images (e.g., dcraw -d output) are used. Specifying this option when a demosaiced image is provided

will not produce the expected result, i.e., you must provide a raw image for this option to work correctly. Keep in mind that

Bayer red and blue each cover only 25% of the sensor, so your edges will have to be 4 times longer to maintain the same

signal-to-noise ratio. Minimum recommended edge lengths are thus 35 pixels for gray or interpolated images, 70 pixels

for green Bayer sites, and 140 pixels for red and blue Bayer sites. Aim for edges of at least 200 pixels for best results on

red and blue sites. See --cfa-pattern so specify the Bayer pattern of your raw image.

--cfa-pattern rggb|bggr|grbg|gbrg

Select the Bayer pattern to use when the --bayer option has been speciﬁed. The default is rggb, which appears to be the