How to Measure Modulation Transfer Function (8)

October 28th, 2014

Now that we know how to apply the slanted edge method, it is time to play around with it and gather some interesting results.

The camera under test is provided with a special lens that has a variable iris setting with a click system, so that it is becoming easy to define and change the F-number of the lens during the measurements. Using a green LED light source with a wavelength of 525 nm, a set of MTF measurements is made at various settings of the F-number. The result is shown in Figure 1.

Figure 1 : MTF measurement for green light, as a function of the F-number of the lens.

While changing the F-number, the exposure time setting of the camera is optimized so that a constant output signal is obtained. For every change of one F-stop, the exposure time is adapted by a factor of 2. As can be seen from Figure 1, starting with a low F-number and moving towards higher values, the MTF increases from F1.4 till F8 and then starts decreasing again till F16. This effect of increase and decrease can be explained by the interaction of three effects :

- Most lens aberrations are becoming worse for lower F-numbers. So changing the lens setting from a low F-number to a larger F-number will decrease the lens aberrations and will increase the sharpness of the image projected on the sensor. Consequently, the MTF will increase,

- Low F-numbers result in larger angles under which the rays are hitting the sensor. If the angle of the incoming rays deviates more from the normal, the chance of generating optical and electrical cross talk is becoming larger. So higher F-numbers result in less cross-talk and better MTF,

- Even with a perfect lens, a point at the object plane will result in a disk at the image plane. This so-called Airy disk has a diameter equal to 2.44xlxF, in which l represents the wavelength of the incoming light. Taking into account a pixel size of 6 um and a wavelength of 0.525 um, the size of the Airy disk is becoming equal to pixel pitch for F4.7, the size of the Airy disk is becoming equal to 2 times the pixel pitch for F=9.4, the size of the Airy disk is becoming equal to 3 times the pixel pitch for F14.1. So if the F-number is becoming larger, the spot size is becoming larger as well and the image at the sensor level is becoming more blurred. This effect is making the MTF lower, which can be observed for a F8 and higher.

The dependency on the F-number is better observable in Figure 2, which illustrates the MTF at 3 different values of the spatial frequency (10 %, 25 % and 40 % of the sampling frequency).

Figure 2 : MTF as a function of the F-number for 3 different spatial frequencies : 10 %, 25 % and 40 % of the sampling frequency, and Airy disk size as a function of F-number.

Also the size of the Airy disk as a function of the lens F-number is shown, referring to the right vertical axis. As can be seen, for green light F8 seems to be the optimum setting of the lens as far as MTF of the camera system is concerned.   More on this topic next time !

Albert, 28-10-2014.

How to Measure Modulation Transfer Function (7)

October 6th, 2014

In the meantime there should be enough explanation about the slanted edge method in this blog, it is time now to do the measurements.  For those of you who want to get quick results with the slanted edge method, you can follow the rules/guidelines/advices of the ISO-12233 standard, buy the testchart, install the software, and get going.  Of course, it is much more fun to develop the whole stuff yourself, and by the way, that is the proper way to learn all the details about the slanted edge method for the MTF characterization.

So now the first measurement results of the slanted edge method will be highlighted.  The various steps to come to the appropriate results go as follows :

  • Focus an object/target with a slanted edge  (preferably between 2o and 10o) on the imager,
  • Grab 50 images of the slanted edge object and average these images to lower the temporal noise,
  • Grab 50 images of a uniform target (without changing the camera settings, without changing the light source) and average these images to lower the temporal noise,
  • Grab 50 images in dark (without changing the camera settings) and average these images to lower the temporal noise,
  • Correct the slanted image data for non-uniformities in dark and for non-uniformities in pixel response and/or non-uniformities of the light source,
  • Select a smaller window of the image in which the slanted edge is present,
  • Calculate the slope of the slanted edge w.r.t. the vertical column or horizontal row direction of the imager, the slope of the slanted edge is needed to calibrate/normalize the horizontal spatial frequency axis of the MTF curve,
  • Record the spatial frequency response (SFR) in 4 adjacent columns, merge the 4 SFR’s and perform a further data interpolation, to get equidistant data point in the spatial domain,
  • Calculate the line-spread function (LSF) based on the 4-times oversampled SFR,
  • Force the LSF through a fast-Fourier transform, resulting in the optical transfer function and calculate the magnitude of the latter to obtain the modulation transfer function,
  • Normalize both axes to get the classical MTF curve.

Figure 1 shows some intermediate steps of the MTF characterization.  The left part of figure 1 illustrates the observed slanted edge, in a window of 100H x 350V pixels.  The slanted edge is created by means of the edge of a MacBeth chart in front of a white sheet of paper.  The middle part of figure 1 shows a randomly chosen horizontal line (in red) along which the dark-light transition is checked.  Through this dark-light transition the pixels values along a vertical column (in green) are used for the SFR measurement.  Finally, the right part of figure 1 shows the calculated slanted edge (in blue).

Figure 1 : Three illustrations of the observed slanted edge : left the raw data coming off the sensor, middle : row and column along which the SFR is measured, right : the slanted edge as calculated by the software tool.

Figure 2 shows the SFR and LSF based on the pixels values shown in figure 1 and after 4 times oversampling of the data (= using the data of 4 adjacent columns).

Figure 2 : Spatial Frequency Response after 4x oversampling.

As can be seen by means of the SFR on figure 2, the transition from dark (left side) to light (right side) is relatively steep, but this steepness is much less visible in the LSF in figure 2.  The latter has to do with the 4x oversampling, which reduces the difference between two neighbouring measurement points.   Also remarkable is the relative large variation in the white background used in the measurement.  But these variations show up at a relative high frequency and will not influence the MTF measurement.

The final MTF result is show in Figure 3.


Figure 3 : MTF obtained by the slanted edge method.

The measurment with white light (R=G=B) results in an MTF of 0.25 or 25 % at Nyquist frequency.  For a pixel with a large fill factor  (the exact value is not known, but the pixel pitch is large and with micro-lenses, a large fill factor can be expected) this number of 0.25 or 25 % is relatively low.  It should be noted that not just the sensor MTF is measured, but the measurement does include the camera lens as well !

Albert, 06-10-2014.

Special Issue of IEEE-ED on Solid-State Image Sensors

September 3rd, 2014

Call for Papers for a Special Issue of

IEEE Transactions on Electron Devices on

Solid-State Image Sensors


In recent years there have been enormous advances in solid-state image sensors in CMOS (CIS).  Improvements in pixel density, quantum efficiency, power dissipation, temporal noise, fixed-pattern noise are just some of the advancements that are permitting the widespread adoption of image acquisition in consumer appliances such as personal digital assistants, digital still cameras, camcorders, cell phone handsets as well as in automotive, industrial, medical and scientific applications.  This special issue will provide a focal point for reporting these advancements in an archival journal and serve as an educational tool for the solid-state image sensor community.  Previous special issues on solid-state image sensors were published in 1976, 1985, 1991, 1997, 2003 and 2009.


Areas of interest include, but are not limited to:


  1. Pixel device physics (New devices and structures, Advanced materials, Improved models and scaling, Advanced pixel circuits, Performance enhancement for QE, Dark current, Noise, Charge Multiplication Devices, etc.)
  2. Image sensor design and performance (New architectures, Small pixels and Large format arrays, High dynamic range, 3D range capture, Low voltage, Low power, High frame rate readout, Scientific-grade, Single-Photon Sensitivity)
  3. Image-sensor-specific peripheral circuits (ADCs and readout electronics, Color and image processing, Smart sensors and computational sensors, System on a chip)
  4. Non-visible “image” sensors (Enhanced spectral response  e.g., UV, NIR, High energy photon and particle detectors e.g., electrons, X-rays, Ions, Hybrid detectors, THz imagers)
  5. Fabrication, packaging and manufacturing (stacked image sensors, back-side illuminated devices)
  6. Miscellaneous topics related to image sensor technology


    Submission Deadline:  February 28th, 2015

    Targeted Publication Date: January 2016



    Guest Editor-in-Chief:

    Prof. dr. Albert Theuwissen, Harvest Imaging, Bree, Belgium, and Delft University of Technology, Delft, the Netherlands.


    Guest Editors:

    Prof. dr. Eric Fossum, Thayer School of Engineering, Dartmouth, NH, USA,

    Dr. Boyd Fowler, Google, Mountain View, CA, USA,

    Prof. dr. Shoji Kawahito, Shizuoka University, Shizuoka, Japan,

    Prof. dr. Pierre Magnan, ISAE, Toulouse, France,

    Dr. Junichi Nakamura, Brillnics, Tokyo, Japan,

    Dr. Johannes Solhusvik, Omnivision, Oslo, Norway,

    Prof. Nobukazu Teranishi, University of Hyogo, Japan, and Shizuoka Univeristy, Japan,

    Dr. John Tower, SRI International, Princeton, NJ, USA.


     Please submit papers by using the website : http:/ , be sure to mention the special issue within the cover letter.

Forum on Advanced Digital Image Processing : update

August 30th, 2014

I would like to give you a quick update of the forum status.  The first session is sold out, but for the second session, there are still some seats available.

For those who are interested, you can find all information at

Albert, 30-08-2014.

How to Measure Modulation Transfer Function (6)

August 4th, 2014

Previous time it was explained that larger angles of the slanting edge may result in deviating MTF values.  The results already presented in the previous post is repeated here in Figure 1.

 Figure 1 : Effect of the slanted edge angle on the accuracy of the evaluation technique to characterize the MTF.

As a message from the simulation results shown in Figure 1 : angles of the slanted edge between 2 deg. and 10 deg. are very well suited for the MTF analysis.  This can be seen by checking their comparison to the ideal curve (see black dots in Figure 1).  Once the angle is larger than 10 deg., the slanted edge method starts loosing accuracy.  The simulation results obtained here are fully in line with the advices of the ISO standard, which suggests also to use an angle of the slanted edge between 2 deg. and 10 deg.  Just to highlight the deviations, an extra insert is included in Figure 1 to shown the MTF behaviour around the Nyquist frequency.

One of the reasons why angles larger than 10 deg. give deviating results is the fact that the number of measurement points in a particular sensor column is getting smaller and smaller if the angle is getting larger.  This can indeed result in nasty effects on the MTF values and can lead to aliasing effects in the sampling of the data.  To avoid these type of issues, it is possible to take the data of multiple columns into account instead of using the data of just a single column.  To show the overall working principle of oversampling, the spatial frequency responses (SFR) of 4 neighbouring columns are shown before (Figure 2) and after (Figure 3) multiplexing the data into a single SFR.

 Figure 2 : Spatial Frequency Response of 4 neighbouring columns.

Figure 2 shows the data collected in 4 neighbouring columns, respectively columns 94, 93, 92 and 91, running vertically and crossing the slanted edge (which has an angle of 15 deg.).  Four SFRs are obtained, all with a relative low amount of data points.  As illustrated in Figure 3, the amount of data points can be increased by means of multiplexing the 4 curves of Figure 2 into one single SFR with 4 times the amount of samples.


Figure 3 : Spatial Frequency Response of the 4-times oversampled data, after multiplexing the 4 curves shown in Figure 2.

Based on this method of 4-times oversampling (also recommended by ISO 12233), the accuracy of the MTF measurement as a function of the angle of the slanted edge is checked again.  The results of this exercise are shown in Figure 4.


Figure 4 : Effect of the slanted edge angle on the accuracy of the evaluation technique to characterize the MTF, based on a 4-times oversampling of the SFR data.

The result is quite remarkable : up to an angle of 20 deg. no deviation between the various obtained MTF curves can be seen, even not in the insert showing the MTF around the Nyquist frequency.

So oversampling when obtaining the SFR is absolutely recommendable, because it results in more data points to generate the SFR.  And in the simulation result described in this and previous blogs, the “measured” modulation transfer function does not deviate from the theoretical one.

Albert, 01-08-2014.

Additional Session for the Solid-State Imaging Forum

July 25th, 2014

Is it the subject of the forum that makes the forum appealing, or is it the speaker that attracts the attention ?  Actually the answer to this question it not that important, I just want to mention that the first session of the forum is nearly sold out, and that is a good reason to organize a second session.  Same location, same speaker, same content, only a different date of course.  The second session is scheduled for DECEMBER 15TH AND 16TH, 2014.

More information can be found on

Albert, 25-7-2014.

Second Solid-State Imaging Forum open for registration

July 15th, 2014

Hello everyone,

All organizational and logistics details are settled, so I can open the registration for the second Solid-State Imaging Forum.  All information of the forum is shown on the website :

Please notice, like last year, I will limit the number of seats to maximum 24.  This will enhance the learning experience.  Only in the case that we get substantially more registrants than this upper limit of 24, a second session can/will be considered.  If you are interested to attend, early registration is recommended for two reasons :

1) for you : to make sure you get a seat (first come, first serve),

2) for me : to get as early as possible an idea whether a second session is needed or not.  (A scond session  can not be organized just a few weeks before the event will take place,)

Thanks, and looking forward to see you at the forum,



How to Measure Modulation Transfer Function (5)

July 4th, 2014

In the last blog the MTF measurement based on the slanted edge was introduced.  As mentioned in that blog, to understand all ins and outs of the method, it is very beneficial to develop a small, simple model of the sensor with a slanted edge projected on it.  And next, analyze the obtained, synthesized image.  This simulation tool is also used here to check out the sensitivity of the technique w.r.t. the angle of the slanted edge.

The result is shown in Figure 1.

Figure 1 : Effect of the slanted edge angle on the accuracy of the evaluation technique to characterize the MTF.

Shown are the MTF results obtained for a simulation of the angle being equal to 2 deg., 4 deg., 6 deg., 8 deg., 10 deg. and 12 deg.  The ideal curve, obtained by the calculation of the sinc-function, is included as well.  As can be seen from the curve :

  • All evaluations based on an angle between 2 deg. and 10 deg. seem to fit very well to the ideal curve,
  • The simulation result for an angle of 12 deg. shows some minor deviations from the ideal curve.

As a message from this simulation : angles of the slanted edge between 2 deg. and 10 deg. are very well suited for the MTF analysis.  Once the angle is larger than 10 deg., the slanted edge method starts loosing its accuracy.  The simulation results obtained here are fully in line with the advice of the ISO standard, which suggests also to use an angle of the slanted edge between 2 deg. and 10 deg.

Next time : how to implement oversampling and how to avoid aliasing effects during the measurements.

Albert, 04-07-2014.

How to Measure Modulation Transfer Function (4)

June 18th, 2014

The MTF or Modulation Transfer Function can be measured in various ways.  In the previous MTF-blogs the measurement by means of a Siemens Star testchart was discussed.  This method has particular advantages, but also has some limitations, mentioned in earlier blogs.  Another evaluation technique to characterize the MTF is based on the so-called slanted-edge method.  Explained in words, this method sounds very complicated, but in reality it is really pretty simple.

There are several good references describing the slanted-edge method, e.g. :

  • M. Estribeau and P. Magnan., in SPIE Proceedings, Vol. 5251, Sept. 2003,
  • T. Dutton et al. in SPIE Proceedings, Vol. 4486, 2002, pp. 219-246,
  • P.B. Burns, in Proceedings IS&T, 2000, pp 135-138,
  • S.E. Reichenback et al. In Optical Engineering, pp. 170-177, 1991.

This slanted edge method became an ISO standard, namely ISO 12233.  This is one of the very few ISO standards for image sensor and/or camera measurements.

The technique of the slanted edge can be described as follows :

  1. Image a vertically oriented edge (or a horizontal one for the MTF measurement in the other direction) onto the detector.  The vertical edge needs to be slightly tilted with respect to the columns of the sensor.  The exact tilting is of no importance, it is advisable to have a tilt of minimum 2o and maximum 10o w.r.t. the column direction.  A tilt within these limits gives the best and most reliable results for the MTF characterization.
  2. Each row of the detector gives a different Edge Spread Function (ESF), and the Spatial Frequency Response (SFR) of the slanted edge can be “created” by checking the pixel values in one particular column that is crossing the imaged slanted edge.
  3. Based on the obtained SFR, the Line Spread Function (LSF) can be calculated, the LSF is simply the first derivative of the SFR.
  4. Next and final step is calculating the Fourier transform of the LSF.  This results in the Modulation Transfer Function, because the MTF is equal to the magnitude of the optical transfer function, being the Fourier transform of the LSF.  Plotting the MTF as a function of the spatial frequency can be done after normalizing the MTF to its DC component and normalizing the spatial frequency to the sampling frequency.

(In one of the coming blogs more info will be given on further improvement and/or sophistication of this procedure.)

A very helpful strategy in understanding how this MTF measurement method works and to check the algorithms, is to run a simulation and create an artificial image with a slanted edge that is sampled by an artificial sensor (e.g. with a pixel fillfactor of 100%).  Next the theoretical, geometric MTF can be calculated as a sinc-function of the spatial frequency, while the synthetic image can be used as the input image to evaluate the MTF by means of the technique explained above (ESF, SFR, LSF, MTF).  Such a simple simulation tool can also be used to check the influence of the various system parameters on the measurement technique.  An example of such a simulation is shown in the following figures.

First of all a synthetic image is generated that results in a slanted edged of 4 deg. w.r.t. the column direction.  A region-of-interest (ROI) of 200 (H) x 300 (V) pixels is created around the black-white transition of the slanted edge.  This synthetic image is shown in Figure 1.

Figure 1 : ROI containing the slanted edge or black-white transition.

A particular column is selected (in this example column number 96), and all pixel values in this column are recorded to generate the SFR or Spatial Frequency Response.  The result of this operation is shown in Figure 2, with reference to the left vertical axis.

Figure 2 : Spatial Frequency Response, being the values of the pixels present in column 96 of the image shown in Figure 1, and Line Spread Function, being the first derivative of the SFR.

Next the LSF or Line Spread Function is generated, simply by numerically calculating the first derivative of the SFR.  The LSF is shown in Figure 2 as well, with reference to the right vertical axis.

Once the LSF is known, the magnitude of the FFT of this LSF is calculated.  Plotting the FFT magnitude versus spatial frequency results in the MTF of the sensor, as shown in Figure 3.  Notice that the MTF is normalized with its value a zero input frequency (= DC), while the spatial frequency is normalized to the spatial sampling frequency of the sensor.  In this simulation example, the pixel pitch is equal to 6.5 µm.

Figure 3 : MTF of the simulated pixel (6.5 µm, 100 % FF), as well as the theoretical, geometric MTF of the same pixel.

In Figure 3 and next to the outcome of the MTF simulation, also the theoretical geometric MTF of the pixel is shown (6.5 µm, 100 % FF), for comparison reasons.  This geometrical MTF is calculated by means of the well-known sinc-function.  As can be seen, both curves coincide very nicely, indicating that the slanted edge method and the algorithms used in the calculation seem to do the job that they were developed for !

Before showing real measurements, in the next blog(s) a few additional improvements of the slanted edge method will be highlighted.

Albert, 18-06-2014.

How to Measure Modulation Transfer Function (3)

April 19th, 2014

A new measurement result in the MTF-series is shown in this blog : the MTF of a monochrome sensor, but no longer with white light input, but with red, green and blue light.  Some interesting observations can be reported.

In Figure 1, the results of the MTF measurement are shown.

Figure 1 : Modulation Transfer Function of a monochrome device for various wavelengths of the incoming light.

It is quite nice to see the influence of the wavelength of the incoming light :

  • The absorption coefficient of silicon for “red” photons, or photons with a lower energy, is relatively low.  The absorption depth for light with a wavelength of 630 nm can reach a few microns.  So part of the electrons generated in the silicon will be generated below the depletion region of the photodiodes, and before these electrons can get collected by the photodiodes, they need to “travel” in the neutral bulk/epi-layer.  Because there is no electrical field present in these regions to guide the electrons to the right photodiodes, the chance that these electrons finally land in a neighbouring pixel is relatively large.  In this way the contrast in the image is reduced, so is the MTF,
  • The absorption coefficient of silicon for “blue” photons, or photons with a higher energy, is relatively large.  The absorption depth for light with a wavelength of 470 nm is just a few tens of a micron.  So most of the electrons generated in the silicon will be generated within the depletion region and the chance of diffusion of these electrons to neighbouring pixels is limited.  The contrast in the image is not reduced by the effect described above for the “red” photons, neither is the MTF,
  • The green light, with a wavelength of 525 nm, has an absorption coefficient situated between the red light and the blue light.  So not surprising that the MTF for the green light is lying between the blue and red results.

The effect explained here by means of the MTF measurements is also known as electrical cross-talk.  The loss in contrast or loss in MTF is due to the diffusion of electrons.  The effect is also illustrated in Figure 2.

 Figure 2 : Illustration of the electrical cross-talk.

Figure 2 shows a cross section of a hypothetical image sensor with an RGB filter.  Illustrated is the fact that the “red” photons can penetrated much deeper into the silicon than the “blue” ones.  This is the origin of the larger electrical cross-talk for the light having a longer wavelength.

To conclude a few numbers :

  • Absorption coefficient for a “red” photon (630 nm) = 4000/cm, resulting in an absorption depth of 2.5 um,
  • Absorption coefficient for a “green” photon (525 nm) = 10,000/cm, resulting in an absorption depth of 1 um,
  • Absorption coefficient for a “blue” photon (470 nm) = 20,000/cm, resulting in an absorption depth of 0.5 um.

Albert, 19-04-2014.