MTFchart-projected (the chart MTF projected on the image sensor) is not really a part of the imaging system, so we’ve dealt with it by recommending that charts be used in conditions (low magnification) where MTFchart-projected stays close to 1 in the frequency range of interest. Since our recommendations have been conservative the results have been “good enough” in most instances.

\(\displaystyle MTF_{sensor} =\frac{ \sin \frac{\pi f}{2 f_{Nyq}}}{ \frac{\pi f}{2 f_{Nyq}}} = \text{sinc} \frac{\pi f}{2 f_{Nyq}}\)  where  fNyq = Nyquist frequency = 1/(2 pixel pitch).

AsphericIOL

Using chart compensation is somewhat more error-prone than not using it. You need to check settings carefully. Make sure

MTFchart-projected is also called MTFdiv because it is used to divide MTFmeasured. The minimum value of the denominator must be greater than 0.3 because smaller values are unreliable and can cause an excessive noise boost. The frequency where projected chart MTF drops to 0.3 should be outside the range of interest for the measurement— above the Nyquist frequency fNyq .

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A recent reference to sensor MTF is Interferometric Measurement of Sensor MTF and Crosstalk (2017) by T. Georgiev, et. al. of Qualcomm, presented at the Electronic Imaging 2017 conference. They used a Ximea MQ013RG-E2 sensor, which has 5.3μm pixels.

Click on a link in the table  to download the chart compensation file for the indicated media type. Save the file to any convenient location. (We recommend the Imatest Resources folder, which can be located by pressing  Open resources folder  in the Chart and sensor MTF compensation or Options II menu.) Although the files contain several lines, only the numbers in the first line (the first line of Key values in the table below) are used for chart compensation. The remaining lines contain annotations (the file used for the calculation, the chart MTF50, etc.) Some of the data is relatively old: we will be taking new measurements.

Lens MTF measurements –  Imatest traditionally measures the MTF of the entire system, lens + sensor + image processing, but a number of customers are interested in measuring the MTF of the lens alone. To do so, the effects of the sensor and image processing must be removed. It’s easy to minimize image processing by converting files from raw  using LibRaw (for commercial files) or Generalized Read Raw (for binary files), but removing the effects of the image sensor is more difficult.  Although exact measurements of sensor MTF are difficult to come by (as of early 2018) we can get a reasonable approximation for many situations (visible light, moderate pixel size) using a simple theoretical equation for geometrical sensor MTF:

These results should not be represented as true lens MTF. At best it’s approximate— closer to true lens MTF than measurements made without the correction, but definitely not all the way there.

Asphericlens meaning

We receive frequent requests from customers who want to measure lens MTF, and it’s always disappointing to tell them Imatest measures system MTF, which includes the effects of the image sensor, and not lens MTF. While sensor MTF can be removed by deconvolution, i.e., the same division process (in frequency domain) used to compensate for the chart MTF, reliable sensor MTF data is difficult to obtain. But even without exact sensor MTF data Imatest can do a partial (approximate) correction for the sensor MTF.

Chart-compensated MTF model –  Chart MTF is measured in units of Cycles per Object mm from a printed edge (appropriately slanted for the measurement), then fit to a simple equation that fits a wide range of chart MTF measurements.

Aspherical lens photography

Here is a typical example, run in Rescharts for a Star chart image. Indicators appear in the y-label, title, and on the middle-right of the Rescharts window. The compensation file name (media type) does not yet appear. Two additional curves appear on the plot. The original MTF without compensation appears as a Magenta dotted line ………..The projected MTF of the chart (MTFchart-projected ) is a cyan dotted line ………..

MTF compensation increases measured MTF values at high spatial frequencies. This often means that noise as well as the signal will be boosted. This is very visible in the above image, taken with a Canon EOS-6D DSLR, which has an anti-aliasing filter that removes most response above Nyquist (~3600 LW/PH). What is left is primarily noise.

If MTFdiv at the Nyquist frequency (fNyq = 0.5 C/P) is lower than 0.9 (90%), measurement accuracy can be improved by dividing the measured MTF by MTFdiv. If MTFdiv(fNyq) is greater than 0.9, there is very little improvement.

To prevent excessive noise boost MTFchart-projected (the cyan dotted line ……….) must not drop too low (to 0.3) in the frequency range of interest.

In Imatest sharpness modules, pixels/mm is typically derived from the user-entered value of pixel pitch (in μm), where pixels/mm = 1000 / (pixel pitch (μm)). Magnification is either entered in the settings window or derived from geometrical factors (like the bar-to-bar spacing in SFRplus or the vertical registration mark spacing in eSFR ISO). We use MTFdiv(f) and MTFchart-projected(f) interchangeably because the measured camera MTF (MTFmeasured) is divided by MTFdiv to obtain the compensated (more accurate) measurement.

We plan to supply MTF compensation files in Imatest builds. They will also be available for downloading in the Reflective charts and Transmissive charts quality pages.

-0.01664, 0.05207, Ver-R -0.01670, -0.04956, Hor-T end_data MTF50{Ver-R), measure:, 19.06, model:, 19.35, C/Obj mm MTF50{Hor-T), measure:, 20.34, model:, 20.54, C/Obj mm file, C:\imatest\Data\SFR\Misc\Chart_compensation\Sony download\Uncertain orientation\SFRplus_LVT_157mm_00019.JPG date_run, 12-Jan-2019 15:59:44 date_mod, 2018-11-05_17-46-40, (closest to capture) Magnification, 1 aperture 8.0 um_per_pixel, 3.88 Equation, MTF = exp(-x(1)*f-(x(2)*f).^2); f in cycles/object mm

*The first key value line contains all information required for the Chart Compensation file. The second line (MTF50 in Cycles/Object mm) is included for reference— for conveniently comparing chart sharpness.

Imatest can correct for the geometrical component of lens MTF in cameras without anti-aliasing filters. Before you apply this correction, you should find out if your camera has one. Most DSLR and mirrorless interchangeable cameras made before 2015 have them. Since 2015 a number of cameras have small enough pixels (sufficient megapixels) to dispense with them with minimal risk of Moiré. Since removing the AA filter significantly improves camera sharpness (beyond the simple megapixel increase) it may be mentioned in the camera specifications and in reviews. For example, see Wired’s review of the Panasonic GX85.

Starting with Imatest 5.1 you can compensate MTF measurements for chart sharpness. Compensation is available in all slanted-edge modules (SFR, SFRplus, eSFR ISO, SFRreg, and Checkerboard), and for Star, Random (Dead Leaves, Spilled coins, etc.), and Log F-Contrast. Applying chart compensation requires care.

For these three modules the chart should be measured carefully. The measurement is entered on the right of the Settings window.

Define asphericlenses

Convolution and deconvolution –  The response of a linear system can be calculated by convolving its components. Convolution is a complex operation— as its name implies— but when response is converted into frequency domain (by means of a Fourier transform), it becomes simple multiplication. The measured response (Modulation Transfer Function = MTF) of an imaging system is the product of its elements:

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If you do not already have Imatest Master, purchase or try a free trial of Imatest Master version 5.1 to use the MTF Compensation feature.

Define asphericeye

Imatest MTF measurements are affected by both chart and camera quality. Since its inception, Imatest has recommended test charts that are large enough to minimize the effects of the chart on camera MTF measurements. Although we have some descriptions of chart quality on the Chart Quality Index, Reflective charts, and Transmissive charts quality pages, these pages don’t have enough detail to determine the precise effect of chart MTF on camera MTF measurements, which is particularly important in situations where geometric constraints (test equipment and lab size, etc.) make it difficult to meet the chart recommendations.

Starting in Imatest 5.1 the effects of the chart can be reduced by dividing the measured MTF by MTFchart-projected, which is equivalent to deconvolution in the spatial domain. We can also calculate the approximate lens MTF by dividing measured MTF by a geometrical model of MTFsensor, which we use because (A) reliable measurements of MTFsensor are difficult to obtain, and (B) results are closer to lens MTF than you can get without the correction.

To apply the lens MTF correction, check the Apply sensor MTF compensation checkbox in the compensation window, shown above.

Chart MTF is measured from images of slanted-edges on various media (inkjet paper, photographic paper, B&W or color film, or Chrome on Glass) at the same contrast (usually 4:1 or 10:1) used for testing lenses. These media are both transmissive and reflective and have a wide range of sharpness.

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When the chart is imaged (projected) on the sensor, the projected chart MTF is calculated by transforming the chart frequency units to the native sensor units (Cycles/Pixel) using

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The actual calculation (details below) is performed with files that contain parametric fits to the measured data for the specific media type and printing technology. Applying chart compensation will improve the consistency of MTF measurements taken on different test charts.

Adimec has a page, CCD vs. CMOS – Modulation Transfer Function (MTF) in NIR, that explains why Sensor MTF is generally worse than the theoretical sinc(πf/(2 fNyq)) model, especially for small pixels and Near Infrared (NIR) wavelengths (> 700μm). It has a plot of  MTF at the Nyquist frequency vs. wavelength for two Sony sensors with relatively large pixels, the ICX674 (4.54μm pixels) and IMX174 (5.86μm pixels). MTF is relatively constant and close to the theoretical value of 0.6366 below 700 nm. The method used to obtain this plot is not stated.

You can create an MTF compensation file using the technique described below in Appendix: Chart MTF measurement. This file should be saved with a descriptive name to any convenient location (though we recommend the Resources folder).

The lines shown in blue are saved to a file, which should have a txt or CSV extension. (If the text isn’t in the clipboard, you can select and copy it.) Only the first line (-0.00968, 0.04781) contains data. The rest consists of comments that you can use to verify that you have the correct settings.

Introduction |  Calculation  |  MTF compensation files  |  Applying the compensation Sensor MTF compensation  |  Chart MTF measurements

For this equation to be valid the sensor must not have an anti-aliasing filter (OLPF) and a raw image must be used (converted with LibRaw or Read Raw). JPEG images from cameras inevitably have signal processing (sharpening and noise reduction) that throws off the results. This approximation is reasonably good for visible light, but poorer for Near Infrared (NIR), where electron diffusion in the silicon degrades the MTF.

Most users won’t be measuring chart quality themselves. They’ll use the measurement results in Chart MTF compensation files provided by Imatest in the above links. Those users can skip this section.