Archive for October, 2014

How to Measure Modulation Transfer Function (8)

Tuesday, 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)

Monday, 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.