Use of the Modulation Transfer Function to Measure ... - IEEE Xplore

Use of the Modulation Transfer Function to Measure Quality of Digital Cameras Miguel E. Bravo-Zanoguera, Javier Rivera-Castillo, Maximiliano Vera-Pérez and Marco A. Reyna Carranza Universidad Autónoma de Baja California, Facultad de Ingeniería Mexicali Blvd. Benito Juárez s/n, Mexicali, B.C. 21900, México Tel. (686)566-42-70 ext. 1315 [email protected] Abstract A test system based on the Modulation Transfer Function (MTF) was developed to measure the quality of the image capture in digital cameras. This method helps to describe image capture performance parameters, as linearity and spatial resolution. The system is composed of an illumination module, a multifrequency sine target, a two axis mechanical support for the digital camera, a three-axis and angular motion support for the sine target, and data processing software. The software was developed under MATLAB for the MTF determination, calculating image contrast at various spatial frequencies. Results are presented for the tests run on three digital cameras: Pentax Optio 450, Sony DSCP41 and Sony DSC-F717.

1. Introduction Commercial optoelectronic equipment like scanners, video camcorders and digital cameras, show the marketing specifications of brand, sensor size, number of pixels in the image and the price, as performance parameters; leaving aside technical specifications. Whereas the technical specifications, for example: number of optical elements, type of electronic sensor, number of pixels used, electronic signal processing, software and compression mode, are factors that affect the equipment performance and its operation. Nonetheless, the urgent need to achieve a specific job, lead us to select devices according only to the available marketing data. This is the reason to undertake the task to determine practical performance measures for digital cameras based on the Modulation Transfer Function (MTF) method; which is a well

established concept for optical systems. Usually, the MTF is used to characterize optical and electro-optical systems.

2. Modulation Transfer Function The MTF measures the capability of a system to capture the information content of an object as a function of the spatial frequencies (Fs), determining image sharpness and resolution. Intensity and contrast in a digital image decreases as the spatial frequency increases, and with the MTF graph is possible to determine the limit of resolution. This limit depends on the characteristics of all the series connected optoelectronic elements. And the system MTF integrates the modulations occurring in all the elements affecting the digital image [1-6]. The system MTF is composed by the multiplication of each element’s MTF conforming it [4,7]. Methods for measuring the MTF are well documented, associating object image, spatial resolution and sharpness [2-6]. However, digital cameras incorporate different technologies that complicates testing, but we still consider the MTF one of the best criteria to determine image quality for these complex imaging devices. Analytically, the MTF is obtained by calculating the modulus of the Optical Transfer Function (OTF) of light distribution on the image plane. The OTF is a complex function obtained from the Fourier Transform of a point object image (spatial spectrum). In general terms is represented as

OTF = MTF ⋅ e iφ( f ) .

(1)

Where the imaginary term φ (F ) represents phase change as a function of Fs, denotation the relative spatial shift of the object frequencies. The drop in

Proceedings of the 16th IEEE International Conference on Electronics, Communications and Computers (CONIELECOMP 2006) 0-7695-2505-9/06 $20.00 © 2006 IEEE

image contrast at higher spatial frequencies is related to the system MTF [9]. Therefore, it is typically adequate to obtain only the modulus of the OTF for performance testing. For a digital camera, the image is a matrix of n × m pixels, where each pixel is an intensity gray level (0 for black and 255 for white) forming the image of the object. The digital camera is a multielement device with a MTF defined by the lens MTF ( MTFL ), the CCD image sensor MTF ( MTFCCD ), and the electronic processing ( MTFe ). Therefore, the system MTF is:

MTF = MTFL ⋅ MTFCCD ⋅ MTFe .

(2)

Both the lens response ( MTFL ) as the CCD sensor ( MTFCCD ) have been developed theoretically [3-7], and they behave as a low pass filter with a resolution given by the size of the lens and the width of the CCD pixel, respectively. The MTFe of the electronic processing depends on the electrical signal conditioning and digital image treatment, which includes image enhancement filters and compression. The MTF, in general, is a plot of the intensity measure in gray level percentage versus spatial frequency (in line pairs per millimeter, lp/mm); resulting in a map of image contrasts for various frequencies. A direct form for measuring the MTF is to use an object with a known spatial frequency (test target) and measuring its image intensity, to calculate image contrast according to the next formula:

M i = Contrast =

I max − I min . I max + I min

(3)

Where Imax is the maximum gray level and Imin is the minimum projected on the image plane by the reference object. The MTF is calculated as follows:

MTF (Fs ) =

M i (Fs ) . Mo

(4)

Where Mo is the object modulation for each spatial frequency considered and Mi is the modulation of the image [3-8]. Mi for each spatial frequency can be calculated as eq. 3. Some methods for measuring the MTF use a test target with calibrated Mo at several spatial frequencies: bar pattern (binary object) or sine pattern (gray levels object) [1,4].

z USB

Illumination

Digital camera

Sine target x y

Computer

x-z positioner

Angle and x-y-z positioner

Figure 1. Alignment system for capturing images.

3. Measuring system development To capture images of the sine pattern object, a lowcost mechanical set-up was mounted on an optical table, accomplishing the fine positioning required in the alignment of the digital camera and the test target planes (figure 1); description follows: a). A dovetail optical rail (Edmund Scientific, No. P54-402) fastened to the optical bench functioned as the main x axis. Two carriers for this dovetail rail (Edmund Scientific, No. P55-340) were used, one to support the digital camera and the other for the test target adaptor. b). A precision vertical translation stage (Edmund Scientific, No. P56-335) attached to one carrier, supported the digital camera, providing micrometer movement. The digital camera adaptor can be displaced in the x- and z-axis. c). An aluminum plate holds in place the sinusoidal test target. This plate is attached to a rotary mounting base plate (Newport Corporation, M-RS65), which provides precise angular adjustment. Also, an adjustable height rack and pinion post, and a rotating adapter plate, completed the elements that allowed the sine target to be positioned in the three axes, besides being able to rotate. All the mechanical adjustments allowed alignment of the sine pattern with respect to digital camera sensor: Image plane parallel to the object plane and positioning of the test target in the field of view of the camera precisely. It is necessary that both planes, object plane and image plane, be aligned as best possible, since the MTF is sensitive to misalignments. A non-constant distance between corresponding plane points introduces defocus information, and an out-ofsequence pixel sampling of the sine waveform, degrade the signal to noise ratio when averaging multiple rows. The illumination source is a 150 watts bulb of diffused white light. The digital images were transferred to a computer, where alignment of the sine pattern was verified, as shown in figure 2.


Read digital image (format JPG).

1

2

3

4 Find in the image the picture square of each spatial frequency.

15 14 13 12 11 10

9

8

7

6

5

Obtain the profile average of each spatial frequency.

Figure 2. Image of the sine pattern target. The number labels relate to frequency listed in Table 1.

Find the maximum and minimum intensity of each spatial frequency signal.

The test target used as object is a reflection card with 15 spatial frequencies (Edmund Scientific, No. 54-804). The gray level intensity of each Fs varies sinusoidal as shown in Figure 2. The characteristics of the pattern are shown in Table 1.

Calculate and normalize the contrast for each spatial frequency.

Table 1. Characteristics of the sine pattern. Region

Fs lp/mm

1

3/16

0.649

2

1/4

0.637

3

3/8

0.638

4

1/2

0.620

5

3/4

0.627

6

1

0.632

7

1,5

0.641

8

2

0.635

9

3

0.642

10

4

0.634

11

5

0.639

12

6

0.631

13

8

0.558

14

10

0.504

15

12

0.446

Draw the graph of MTF vs Fs.

M0 Modulation

The digital image is composed by three matrices, one for each primary color. One of these is picked to carry the gray level contrast analysis on each Fs region of the sine target. An average profile is obtained for every region, resulting in 15 different sine profiles to determine the maximum and minimum intensity values. These intensity values are applied to equations 3 and 4, generating 15 points for a MTF graph. The software GUI was developed in MATLAB to process the images via a multi-region selection, and to calculate and plot the MTF vs. Fs. The flow diagram is shown in Figure 3.

Figure 3. Flow diagram of the software. The digital cameras tested were a Pentax Optio 450 (camera A), a Sony DSC-P41 (camera B) and a Sony DSC-F717 (camera C). Some of the specifications of these cameras are presented in Table 2. Table 2. Specifications of the digital cameras. Model Size of the CDD

Camera A Pentax Optio 450 4.1 M pixels

Camera B Sony DSC-P41 4.1 M pixels

Camera C Sony DSC-F717 5M pixels

(2288ɯ1712)

(2304ɯ1728)

(2560ɯ1920)

Optical components

9 elements in 7 groups and two aspheric elements

4 elements in 5 groups and one aspheric element 2

5 elements all lenses are Carl Zeiss

Optical zoom Digital zoom Quality

5x

3x

5x 2

4x

3.6x 2

5x 2

Best, better and good

Fine and standard

Fine and standard

Automatic

Automatic

Automatic

1.5”

1.5”

1.8”

Capture. LCD display

1

1. Specifications obtained from the product manual unless otherwise stated. 2. Specifications obtained from website www.dpreview.com/reviews/specs/Sony/


Digital cameras have some degree of image sharpening to make the JPG images look good. Usually sharpening increases the 50% MTF frequency (MTF50), which correlates strong with perceived image sharpness [10]. To compare different cameras on fair basis the sharpening feature was set to default.

4. Results Under the same illumination conditions, alignment of the sine target, image of the object fully enclosed in the LCD screen (figure 2), and with the best quality compression mode set, images were captured in high resolution for each digital camera. Although these experimental conditions resulted in better magnification for the Sony DSC-P41 camera, while the other two had approximately equal magnification. After transferring the digital images to the computer, these were processed with the software developed under Matlab to calculate the MTF (automation of eq. 3 and 4). The results are shown in figure 4. Usually, the resolution limit is considered at the spatial frequency where the MTF curve crosses 0.1 of the normalized magnitude; this point is considered the maximum frequency of the system. From the plots of figure 4, it can be appreciated that up to a frequency of 1.0 lp/mm, the three cameras behave in a similar linear fashion; with the MTF decaying from its initial value. In the next middle frequencies, the response of cameras A and B increases significantly, representing amplification of the intensity of those spatial frequencies that conforms the objects in the image. While camera C maintains its response almost constant in an ample range of frequencies.

point, the MTF diminishes gradually from 0.866 down to 0.0597 in the frequency of 6 lp/mm. From the MTF graph it is deduced that the images captured with the digital camera A provided better contrast in a wider range of frequencies in comparison with camera B. For digital camera A, a bandwidth near 6 lp/mm can be considered, since it looses definition at spatial frequencies beyond 5.5 lp/mm. The MTF outline for digital camera B (*) reaches its maximum value (0.881) at a frequency of 1.5 lp/mm, and in following points the MTF decays almost linearly to 0.144 at the spatial frequency of 4 lp/mm. The outline of the MTF shows that the images captured with digital camera B, provide best contrast in the middle frequencies, losing definition approximately beyond a frequency of 4 lp/mm. For this digital camera we can consider a bandwidth close to 5 lp/mm, under the conditions established at the time of the capture. The MTF outline for camera C (o) reaches its maximum value of 0.613 at a frequency of 0.18 lp/mm. After that point the response is approximately constant until the frequency of 4 lp/mm. Then the MTF decreases gradually to 0.043 at the frequency of 8 lp/mm. In the range of 0.25 to 4 lp/mm the variations of the response are small, therefore we can even consider an almost flat response of the digital camera; this is, the same contrast exists in this range of spatial frequencies. After the frequency of 4 lp/mm, the MTF decays linearly, losing its definition at frequencies frequency close 8 lp/mm. For this digital camera it is possible to consider a bandwidth near the 8 lp/mm, outperforming the other two cameras in resolution. In another experiment, an analysis of the MTF on sections of the captured image area was made solely to the Pentax Optio 450 digital camera. The procedure consisted in dividing in three regions (a, b and c) the LCD screen of the digital camera (figure 5), and performing the MTF measurement of each region.

LCD display

Region a

Figure 4. Graph of the MTF of three different digital cameras. The MTF plot of digital camera A (+) has its maximum value at frequency of 2 lp/mm. After this

Region b

Region c

Figure 5. LCD screen of the digital camera. Images of all the Fs of the sine target were captured in each region of the LCD and processed; the results of MTF by region are shown in figure 6. It is


observed that responses in the regions “a” and “b” of the digital camera are similar up to 3 lp/mm; the contrast for the middle spatial frequencies are equal in both regions. Although region “c” presents less contrast in middle frequencies, the resolution of the three regions is approximately at he spatial frequency of 5.5 lp/mm. The bandwidth is approximately equal for the three regions.

Figure 6. Graph of the MTF by screen region of the digital camera Pentax Optio 450.

5. Conclusions A low-cost system for the MTF evaluation of digital cameras has been developed, which includes an illumination and mechanical alignment set-up. With the use of standard math software, a tool for multiple image regions selection generated MTF curve points; averaging of multiple rows produced a fair S/N measurement. This development addresses the need for an MTF regional laboratory. Although important, the number of image pixels it is not sufficient to define the quality of the image captured by a digital camera. The number of pixels of the electronic sensor and the quality of optical elements that a digital camera has are reflected in the performance. Although cameras A and B both are of 4.1 Mpixels and they have correspondence in their respective plot of the MTF, the bandwidth of camera A (approximately 6 lp/mm) is greater than the one of the camera B (close to 5 lp/mm). Digital camera B provides a high contrast to the digital image in a small range of the middle spatial frequencies. The images captured with this camera do not have fine details. The digital camera A has a greater bandwidth than camera B. It also increases the contrast of the digital image in the range of middle frequencies. The images captured with digital camera “A” have more fine details than the images captured with digital camera B.

Digital camera C, with 5 Mpixels in its electronic sensor, provides a roughly constant response to a wider range of spatial frequencies (bandwidth of almost 8 lp/mm); therefore, the digital image has a regular contrast for the spatial frequencies that compose the image. The images captured with digital camera C have more fine details than the images captured with the digital cameras A or B, indicating its potential. We can conclude that the marketing information of brand, size of the electronic sensor in pixels, size of the image in pixels and price provided by vendors, is not enough to select a camera for use in a specific application. Therefore, it is convenient to have specialty labs evaluating the performance of digital camera systems. Different manufacturers have different measurement procedures, and making a purchasing decision using different manufacturer's MTF charts is not recommended. A camera with extreme over sharpening correlates strongly with perceived image sharpness but may have poor image quality. Comparisons between digital cameras should be based on a full MTF evaluation using the same procedure.

References [1] D. Williams, RLG DigiNews, ISSN 1093-5371, Feb. 15, Vol. 7 (1), 2003. [2] P.B. Greer y T. van Doorn, Evaluation of an algorithm for the assessment of the MTF using and edge method. Med. Phys. 27 (9), pp 2048-2059, 2000. [3] J.M. Boone, T. Yu, y J.A. Seibert, Sinusoidal modulation analysis for optical system MTF measurements. Med. Phys. 23(12), pp 1955-1963, 1996. [4] Glenn D. Boreman, MTF in Optical and ElectroOptical Systems, SPIE Optical Engineering Press, Bellingham, WA, 2001 [5] PIXEL PHYSISCS, CCD and CMOS focal plane array testing, Application Note. [6] D. Williams y P.D. Burns, Diagnostics for digital capture using MTF. Eastman Kodak Company. [7] Gerald C. Holst, Sampling, Aliasing, and Data Fidelity. JCD Publishing, 1998. [8] Glenn D. Boreman, Basic Electro-Optics for Electrical Engineers, SPIE Optical Engineering Press, Bellingham, WA, 1998. [9] Douglas B. Murphy, Fundamentals of Light Microscopy and Electronic Imaging. Wiley-Liss, Inc. 2001. [10] www.imatest.com/docs/sharpening.html
