Relationships between lens performance and different sensor sizes in professional photographic still SLR cameras

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1 Relationships between lens performance and different sensor sizes in professional photographic still SLR cameras Carles Mitjà a, JaumeEscofet b, Fidel Vega b a CITM/UPC, Campus de Terrassa, Edif. TR12, Terrassa, Barcelona, Spain. b Dept. of Optics and Optometry, UPC, Campus de Terrassa, Edif. TR08, Terrassa, Barcelona, Spain ABSTRACT Current photographic still cameras, in the professional SLR step, are available in two basic sensor sizes, 16x24mm and 24x36mm and both of them can be used with the same or similar range of focal length lenses. Lens aperture determines resolving power and diffraction effects and indeed, MTF function. In order to preserve an acceptable image quality level, it must be taken into account that a high lens resolving power at larger apertures can be replicated by the sensor as a false response or aliasing, while the size of the Airy disc must be related with photo receptors pitch. Provided that a standardized metric of image quality is the system MTF, this work compares different lenses resolving power as a function of aperture with the lens and system MTF; both aliasing and resolution affectations can be observed in the system MTF. Lens resolving power has been measured by visual inspection of the aerial image of an USAF1951 test target through a suitable microscope. The lens PSF and MTF has been measured by means of a Shack-Hartmann optical wave front sensor. The system MTF is measured by the slanted edge method. The different experimental procedures have been applied to two professional SLR cameras equipped with the same general use lens. Keywords: PSF, MTF, Strehl ratio, cut-off frequency, Nyquist frequency, aliasing, image quality. 1. INTRODUCTION Digital photography has evolved very quickly in the last years. Every day new products with more improvements appears in the market targeted to prosumer as well as professional segments. Nowadays, several professional SLR camera lines offers different camera bodies equipped with sensors of two sizes around 15x23 mm and 24x36 mm. Both sensor sizes are offered with several number of photo receivers and, consequently, the photo receiver size and the limiting system resolving power or Nyquist frequency are quite diverse, even between the same brand models; pixel pitch can be found from 5.4 up to 8.5 m. All of those camera bodies must be equipped, with few exceptions, with the same set of lenses. Because of the wave nature of light, a diffraction-limited photographic lens with a finite sized aperture, images any object point as an spot, the Point Spread Function (PSF); in such a situation and in absence of image aberrations, the PSF has a characteristic minimum blur diameter, as a function of the object distance, the aperture diameter and the light wavelength. If the system has a circular pupil the PSF is the Airy disc. In the frequency domain, the Optical Transfer Function (OTF) is to be defined as the Fourier Transform (FT) of the PSF. In diffraction-limited systems the OTF is the normalized autocorrelation of the exit pupil. The Modulation Transfer Function (MTF) is the modulus of the OTF. The MTF curve shows the lens performance by rating the contrast between the object and the image for a different set of frequencies. The MTF is a commonly used metric that defines the spatial resolution characteristics of an imaging system. This metric provides information about how much contrast is lost when light passes through an optical system for each spatial frequency up to the cutoff frequency. For a diffraction-limited system with a circular exit pupil, the MTF is 1 : 2 MTF( f ) = arc cos f f 0 f f 0 0 Otherwise f 1 f 0 2 f f 0 (1) Current Developments in Lens Design and Optical Engineering X, edited by Pantazis Z. Mouroulis, R. Barry Johnson, Virendra N. Mahajan, Proc. of SPIE Vol. 7428, 74280P 2009 SPIE CCC code: X/09/$18 doi: / Proc. of SPIE Vol P-1

2 Being f 0 the cutoff frequency and its value is: f 0 = 1 N 1 + m ( ) Where is the wavelength, N the diaphragm number and m the working lateral magnification. In the case of a photographic lens with, i.e., a maximum aperture of N = 4, an object at the infinity (m = 0) and = 555 nm, the cutoff frequency is f 0 = 450 cycles/mm. For a minimum lens aperture of i.e., N = 32 and the same conditions, the cutoff falls down eight times achieving a value of f 0 = 56.3 cycles/mm. According the Rayleight criterion, the lens resolving power (RP) is calculated as: RP = f 0 (3) 1.22 A single parameter associated with image quality of an optical system is Strehl ratio. It is defined as the ratio between the on axis PSF obtained from the system to the on axis PSF of a diffraction-limited system with the same N value 2 ; this is the same that the ratio between the area under the system MTF curve to the area under the corresponding curve of a diffraction-limited system. Excellent image quality is expected when Strehl ratio exceeds 0,80. There are several methods for measuring the MTF of an optical device, discrete or continuous frequency generation, image scanning and wavefront analysis 3. Recent advancements in precision mechanics and electro-optics technologies have produced many practical derivations of these methods that allows efficient measurement of OTF with very high accuracy 2. All of these methods require sophisticated equipment, optics, mechanics and software. In diffraction-limited systems, MTF function is fixed when f 0 is known. Indeed, this cutoff frequency can be measured without sophisticated optic equipment as lens MTF function demands. In this case only a good magnifier is needed in order to resolve, by visual inspection of the aerial image of a USAF1951 or sinusoidal test chart formed by the system. Because of the discrete characteristics of the image sensors, CCD or CMOS in the professional SLR cameras, sampling is an inherent feature of those devices. What sampling means is that the continuous image illuminance can only be represented as discrete pixels or picture elements, which arise from the discrete locations of the sensor photo receivers. The sampling worst effect is the aliasing and it is most noticeable on image edges, where it causes jagged shapes and in periodic features, where it causes Moiré patterns, both of them degrades the image quality. This sampling creates limits on what images can be reproduced faithfully. Specifically, the sensor Nyquist frequency, or f N, is the maximum spatial frequency that can be imaged without causing artifacts, that is, is the sensor cut-off frequency. The Nyquist frequency of the camera is defined to be equal to one half of the sampling rate. If a higher signal than Nyquist frequency is present in the imaged scene, it will be aliased, or made to look like a lower frequency as a response in the registered image. In general photographic systems, the lens cut-off frequency is greater than the sensor Nyquist frequency. This means that the sensor fixes the system s cut-off. In the extreme case with the objective at minimum aperture, the cut-off may be fixed by the PSF. In this case no aliasing effects can be observed, but the diameter of the lens PSF may be greater than the pixel pitch and that means that the effective resolution in the image is lower than expected. To counteract the aliasing, many digital cameras have an anti-aliasing filter to cut out the high frequency components of the image. The ideal filter would simply multiply all frequencies up to the Nyquist region by one, leaving them unchanged, and multiply all frequencies above the Nyquist frequency by zero, thereby eliminating them. This kind of filter is impossible to implement as a practical device, but it may be approximated. Some optical low pass filters has been used as small diameter aperture, defocusing, image blur or birrefringent materials over the sensor 4. Currently, many professional SLR cameras indicates to be equipped with low pass anti-aliasing filters of birrefringent materials mounted together with the infrared filter and the photo receivers micro lens and Bayer filters set. In a photographic camera, the system MTF is the result of multiplies the different steps MTF from lens to the final image file. There are a variety of methods to measure the system MTF. The function can be derived from measurements of the modulation of an USAF1951 test target imaged by the system 5. A second approach is to extract modulation data from the image of a sinusoidal test target image obtained trough the system to be tested. The so-called slanted edge method uses an edge imaged by the system from which is possible to extract frequency and amplitude data 6. Finally, a random target of known spatial frequency content allows measurement of a shift invariant MTF 7. (2) Proc. of SPIE Vol P-2

3 This work compares the system performance of two different SLR camera bodies equipped with the same lens at different aperture values. The basic differences between them are the sensor size and the number of photo receivers, in addition of five years of technological evolution. The lens is a suitable close up unit from the same cameras brand; its performance is optimized for an m = 0.1. This comparison is derived from the measure of the lens resolving power, PSF, MTF and Strehl ratio; the system MTF is measured by the slanted edge method and the image of a sinusoidal test pattern is analyzed to detect aliasing effects. In Section 2, device characteristics and measurement methods employed are presented. Sections 3 and 4, shows respectively, results and conclusions. 2. MATERIALS AND METHODS 2.1 Cameras and lens The camera bodies used in this work are the Nikon D70 and the Nikon D700. These cameras represent two different approximations to the advanced amateur and professional levels respectively in addition to five years of technological evolution. The D70 body is equipped with a CCD sensor of 15.5x23.7 mm in size and 2000x3008 photo receivers; as stated on camera specifications, the sensor uses a color filter array (CFA) with Bayer pattern and is covered by an IR blocking filter and anti aliasing filter of birrefringent material. The D700 body incorporates a CMOS sensor of 24x36 mm in size (so called full frame in reference to the former 35 mm film) and the same specifications related to the CFA, IR and anti aliasing filter. Both camera bodies offer the possibility to capture in several JPEG quality levels and RAW files under the suffix.nef (short for Nikon Electronic File) with (so called lossless option) or without compression. The bit depth is adjusted by default to 12bit in the D70 body; in the D700 camera body there is the possibility to choose between 12 or 14 bit depth. The Table 1 shows a compendium of cameras characteristics. Table 1. The table shows some specifications of the Nikon D70 and D700 bodies used in this work. Camera body Sensor Sensor size Photo receivers Nyquist Frequency Bit depth CFA pattern Nikon D70 CCD 15.5x23.7mm 2000x lp mm bit Bayer Nikon D700 CMOS 23.0x36.0mm 2832x lp mm or 14 bit Bayer The lens mounted is the same for the two camera bodies. The unit is a Micro NIKKOR 55mm f/3.5 from Nippon Kogaku. The design is near symmetric and there are no floating group lenses for the focusing operations, but the whole unit is moved closer or far away from the camera body by means a suitable helicoidally designed focusing mechanism. The specification sheet states that the lens is optimized for a magnification of m = 0.1, and this is the value used for all described tests. The aperture scale goes from f/3.5 to f/32; the different comparative test has been done using only the integer aperture values from f/4 to f/ Image files All image files used in this work have been captured using electronic flash strobes as illuminant with a color temperature of 5600ºK that ensures exposure times shorter than 1/250 s and avoid undesired effects because of camera shaking during the exposure. The proper exposure at the different aperture values was adjusted by means of the strobes output using in strobe regulators and/or neutral density filters in front of the strobe lamps. The file format used was RAW without compression in both cameras; the bit depth has been adjusted to 12 bit (default) for the D70 body and 14 bit in the D700 camera body. The files have been processed with the Adobe Camera Raw (ACR) tool from Adobe Photoshop CS4. The ACR aperture profile used is a specifically designed one keeping the basic characteristics of the captures untouched, that is, any change in brightness, tone, color or contrast are applied; the luminance transfer map is linear and all in camera and ACR sharpening and noise reducing tools were cancelled. Both cameras and software color space was Adobe 1998 and the bit depth output options were adjusted to 16 bit, as is standard in professional work. After ACR processing, the files were converted to 8 bit grayscale mode and TIFF format using a weighted scheme for the channels average of 0.299R, 0.587G, 0.114B. Proc. of SPIE Vol P-3

4 2.3 Lens resolving power The lens resolving power at the different aperture values available, were measured by visual inspection of the aerial image formed by the lens of a transmission USAF1951 test target from Ealing, with the aid of a suitable tube microscope with a magnification of 100x. A great magnification power is necessary because of the high lens resolving power, up to 320 lp/mm, at wider aperture values. The test was uniformly illuminated by transmission through a white plastic diffuser with a tungsten lamp. Both the test and the lens under testing were attached to an optical bench from Sinar AG by means of stands with micrometric adjustment knobs that ensure the proper planes relationship and allow adjusting thoroughly the involved distances. Since all measures were done in the on axis region, the mounting must allow for the proper centering of the target element involved in each case with the center of the lens field of view and the center of the microscope field as well. The complete mounting is shown in Figure 1. Fig. 1. Set up for the measurement of the lens resolving power. Longitudinal distances may be properly fixed in order to achieve the required lens magnification. The USAF1951 test target is fixed on a stand that allows for lateral and rise displacements in order to center each target element with the lens field of view; correspondingly, the microscope can be too risen or shifted as necessary to center its field of view with the test target aerial image. 2.4 Hartmann Shack The measurement of the wave front aberration of the objective is made with a commercial Hartmann-Shack wave front sensor (HASO3 wave front analyzer from Imagine Optics). A single mode optical fiber (core diameter 12 m) is used as the object point source. The fiber is placed at the distance of 605 nm, which, in our case, is the distance that allows for the magnification with optimum lens performance. Hartmann Shack Single-mode fiber Lens under test wavefront sensor Microscope objective 4X L Fig. 2. Set up for the measurement of the lens PSF and MTF with indications of each component. An object point sourced by a single-mode optical fiber passes through a microscope objective and is imaged by the lens under testing on the Hartmann Shack sensor, which software provides data of the lens PSF, Strehl ratio and MTF among many other measures. Proc. of SPIE Vol P-4

5 The point spread function (PSF) of the objective is calculated with the commercial software associated to the HASO. The software calculates the energy distribution at the focused point of the beam by back-propagation of the Fourier Transform (FT) of the complex pupil function: PSF ( r i, i ) FT P ( r, ) e i 2 W ( r, ) (4) Being P(r,) and W(r,) the amplitude and wave front aberration measured with the HASO wave front sensor. Since the PSF has been filtered by the lens of some of the spatial frequencies that originally composed the object source point, its FT shows what spatial frequencies remain and at what contrast. Therefore, the FT of the PSF produces directly the modulation transfer function (MTF). The experimental set up is shown in the Figure Sinusoidal test target In order to detect some possible effects of aliasing in the images taken for each camera, a sinusoidal test target from Edmund Optics (Figure 3) was imaged with both cameras at all the range of lens apertures available. The test was transilluminated in the same manner described for the USAF1951 test in the lens resolving power procedures. Nevertheless, in this case the lighting source employed was an electronic flash strobe by the reasons explained in the Section 2.2. I'll'- IUUhIIIII Li I I I I Hii noun U a Jo t'9 Ut, 0t LIJIU/dI L S wwidi 05 SE L 0 5? o a 0 L LU? 0 IL P0 0? 91 DL L 1UtUJ Fig. 3. Image of the sinusoidal test target from Edmund Optics (left). The test encompasses a series of gray patches in the upper and bottom rows; the two central rows are a series of sinusoidal waves of progressively higher frequency. At left of the third row, there is a black and white bar pattern to measure the modulation achieved by the image. At right, the test target scheme with a red arrow indicating the sinus pattern of 6 lp/mm; at the magnification used in the experimental set up, this the last pattern that should be resolved by the camera systems on trial. The proper exposure for all taken pictures was selected to achieve a high gray level value just below saturation in the transparent patch of the sinusoidal test target (Figure 3). Several gray values plots on the patches near the Nyquist frequency of each camera were taken to compare the performance of the respective anti aliasing filters. 2.6 Slated edge MTF measurement The MTF function of each system was measured by the slanted edge method using the plug in SE_MTF 8 from ImageJ. The plug in provides image modulation up to the Nyquist frequency. The test used is a black to white edge slightly slanted respect the system sensor grid of photo receivers (Figure 4). The test was created by graphic process; a black rectangle was imprinted on a white glossy photographic quality paper with a high quality inkjet printer. The test was properly mounted at the correct distance from the camera and evenly illuminated with two electronic flash strobes. All exposures were taken just below saturation of the white test region U LU LU I; Proc. of SPIE Vol P-5

6 Fig. 4. Set up for the system MTF measurement. The SLR camera under testing is mounted on a micrometric stand attached to the same optical bench than the slanted edge test; the bench provides suitable relative centering and distance. The bellow protects the lens from undesired light. 3. RESULTS 3.1 Lens resolving power Micro Nikkor 55mm f/3.5 lens resolving power results are shown in Figure 5 at the whole range of integer aperture values. The results obtained are always slightly below the expected theoretical value for such a magnification and a wavelength of 555 nm; nevertheless, the differences are minimum taking into account the discrete character of the USAF1951 test target and the wavelength used in the theoretical calculations compared with the illuminant employed in the experimental set up. As explained in the Nikon literature, the lens is near diffraction-limited behavior Micro Nikkor 55mm f/3,5 4 5, aperture value Diffraction limited resolution Lens resolution Fig. 5. Actual Micro NIKKOR 55mm f/3,5 lens Resolving Power as a function of aperture value compared with the diffraction limited resolving power calculated for = 555 nm. Proc. of SPIE Vol P-6

7 3.2 Lens PSF and Strehl ratio The PSF derived from the Hartmann Shack measures show the increase of the Airy disc as a function of the aperture diameter. The Strehl ratio (SR) value is always higher than the 0.80 expected value for an excellent image quality. f/4 f/5.6 f/s f/fl f/1 SR-ø.86 SR=e.92 SR=ø.96 SR=e.94 SR=ø Fig. 6. Series of PSF plotted from the Hartmann Shack experimental set up, with indication of the aperture and Strehl ratio values. The PSF shapes show the effects of diffraction on the Airy disc diameter due to the size of the aperture; the best SR value is the corresponding to the f/8 aperture. 3.3 Lens MTF The lens MTF curves from the Hartmann Shack experimental set up, show in all cases a shape very close to the predicted values. The different limiting frequency values for the range of apertures available are always above the Nyquist frequency of the two camera bodies on trial, with only one exception for the f/32 aperture. 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 MTF Micro Nikkor 55mm f/3,5 lens LUUUIUUUUBUUIIU EiUUUUUUUUUUUUUU ;uuuuuuuuuuu i iuuuuuuuuuu I + iiuiflhiuuuii uuc uuiuuuuu /'t0' D70 frequency (cycles/mm) * ff4 f/5,6 f/8 " f/il f/16 f/22 + f/32 Fig. 7. Micro NIKKOR 55mm f/3,5 lens MTF at different aperture values. Red arrows indicate the respective Nyquist frequency for the two camera bodies tested, Nikon D700 (59 cycles/mm) and Nikon D70 (63 cycles/mm). The MTF curve corresponding to the f/32 aperture is coded with blue crosses indicating that the lens limiting frequency is below (44 cycles/mm) the Nyquist frequencies of both camera bodies. 3.4 System MTF The system MTF measured by the slanted edge method for the whole set of aperture values available, shows a different behavior for each system. With the D70 body, the system responds almost identically for all apertures from f/4 to f/16 showing high modulation factor values up to 0.20 in the Nyquist region; this claims for aliasing with those apertures which lens resolving power is clearly above the system Nyquist frequency. The modulation factor of the curve corresponding to the aperture value of f/22 drops down until a value of 0.10 at Nyquist; the resolving power of the lens at this aperture value is only slightly above the system Nyquist frequency. Finally, the curve corresponding to the aperture value of f/32 shows, as expected, a loss in resolution due to diffraction (Figure 8). Proc. of SPIE Vol P-7

8 MTF L1 Nikon D70 body with Micro Nikkor 55mm f/3,5 lens 1,0... 0,8..u ,5 0,4 0,2 0,1 uum 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,4S 0,50 frequency (cycles/pixel) -f14 to f/16 F/22 -f/32 1,0 0,8 0,0 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 MTF Nikon D700 body with Micro Nikkor 55mm f/3,5 lens 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 frequency (cycles/pixel) - f/4 to F/22 - f/32 Fig. 8. MTF curves corresponding to the D70 (left) and D700 (right) systems tested. The curves of the D70 system show similar values for the range of apertures from f/4 to f/16, claiming some aliasing effects at the Nyquist region; the system improves the response for the f/22 aperture and shows a predictable loss in resolution for the f/32 aperture value due to diffraction. The curves from the D700 system are very similar for the apertures from f/4 to f/22, don t being suspicious of aliasing phenomena; the curve of the f/32 aperture shows the same drop in resolution that the D70 system. The measures from the D700 camera show similar shapes for the aperture values from f/4 to f/22, with modulation factor values around As in the case of the D70 camera, the curve of the f/32 aperture drops down showing the loss of resolution by diffraction. The comparison between systems appears to indicate a better performance for the anti aliasing filter in the case of the D700 camera. Nonetheless, the action of the anti aliasing low pass filter affects too to the medium and low frequencies resulting in a worse general MTF curve shape, while the D70 system maintains better medium frequency modulation values. 3.5 System Aliasing The system aliasing analysis depicts a clearly different response from the two tested cameras. Figures 9 and 10 show plots of pixel gray value from the sinusoidal test target captured by the two systems. The plots corresponding to five sinus patterns from the complete range of apertures available; from left to right, the two first patterns having frequencies below the system limiting frequency, the central pattern is the last to be resolved by the system and the next two having frequencies beyond the system Nyquist frequency. The Nikon D70 camera shows a lower than expected frequency on the last pattern to be resolved from the apertures f/4 to f/22; this claims for overlapping beat frequency due to aliasing; in addition, significantly modulations can be observed in the patterns beyond the system Nyquist frequency from f/4 to f/16. As expected, the plot corresponding to the f/32 aperture shows no response at the last pattern to be resolved plot because of the lower than Nyquist frequency input (44 cycles/mm). The D700 system exhibits a distinctly behavior. A low contrast overlapped beat frequency can be observed in the last pattern to be resolved plot from f/4 to f/22. Any significant response is present beyond the system Nyquist frequency. As in the D70 system, the D700 camera does not resolves the pattern of 55 cycles/mm at f/32 due to the loss of resolution in the input signal by diffraction. As explained before from the plots of the two systems MTF, the D700 camera shows a better performance of the low pass anti aliasing filter than the D70. From the sinusoidal test plots can be derived too that the image modulation for the patterns below but closer the system Nyquist frequency is better for the D70 camera, as have been shown by the corresponding system MTF plots. Proc. of SPIE Vol P-8

9 Fig. 9. Plots of pixel gray value from five sinusoidal patterns captured with the D70 camera; from left to right, two patterns with frequency below the system Nyquist frequency, the last to be resolved (56 cycles/mm) and two beyond the system limiting frequency. All set of plots were taken with the complete range of apertures available, from f/4 to f/32. Proc. of SPIE Vol P-9

10 Fig. 10. Plots of pixel gray value from five sinusoidal patterns captured with the D700 camera; from left to right, two patterns with frequency below the system Nyquist frequency, the last to be resolved (55 cycles/mm) and two beyond the system limiting frequency. All set of plots were taken with the complete range of apertures available, from f/4 to f/32. Proc. of SPIE Vol P-10

11 4. CONCLUSIONS 4.1 Lens testing The methods used for the previous lens testing have been proven as well correlated in its results. For the complete range of apertures available, the same behavior is shown by the PSF derived from Hartmann Shack measures and the resolving power tested by aided eye inspection of the USAF1951 test target image. The lens MTF and the corresponding limiting frequencies are closely coincident with those obtained by the lens resolving power test. 4.2 Systems MTF The determination of the system MTF by the slanted edge method is a valuable and easy to use procedure to achieve a general vision of the system image quality performance. From the results of this work can be assessed that the values of the modulation factor in the Nyquist region are well related with the suspicion of anti aliasing filter malfunction. This intuition should be related with the lens resolving power for each aperture value. 4.3 Systems aliasing From the results can be derived that the capture of a sinusoidal test target in order to confirm the suspicion of possible aliasing detected by higher than normal modulation factor values in the Nyquist region of the system MTF, is a well suited procedure. Such a test is very explicit about the system response to below but closer or beyond the Nyquist frequency input signals. As a final conclusion appears the fact that an efficient anti aliasing behavior is a trade-off between the suppression of higher than resolvable frequencies at the expense of a moderate performance for the system detectable range of detail. ACKNOWLEDGEMENTS To Fundació Politècnica de Catalunya. To MEC and FEDER (Project DPI ) to support this work. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] Goodman, Joseph W., Introduction to Fourier Optics. McGraw-Hill Optikos Corporation, How to Measure MTF and other Properties of Lenses, Boreman, Glenn D., Modulation Transfer Function in Optical and Electro-Optical Systems. SPIE Press Holst, Gerald C., CCD Arrays, Cameras, and Displays, JCD publishing, Winter Park FL, Sitter, D. N., Goddard, J. S., and Ferrell, R. K., (1995), Method for the measurement of the modulation transfer function of sampled imaging systems from bar-target patterns, Applied Optics, v. 34 n. 4, pp Burns, P.D., Slanted-Edge MTF for Digital Camera and Scanner Analysis, Proc.IS&T 2000 PICS Conference, pg , Daniels, A., Boreman, G. D., Ducharme, A. D. and Sapir, E., Random transparency target for modulation transfer function measurement in the visible and infrared regions, Opt. Eng. 34, , Mitja, Carles and Revuelta, Raquel. Slanted Edge MTF measurement plug in for ImageJ. Proc. of SPIE Vol P-11