SPIE Proceedings [SPIE 5th International Symposium on Advanced Optical Manufacturing and Testing...

Modulation transfer function measurement of sampled imaging systems in

field test Yang Lea,b,Sun Qianga,Wang Jiana,Zhang Jianzhonga,b

aChangchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033,China;

bGraduate School of Chinese Academy of Sciences, Beijing 100049, China ABSTRACT

A digital mirror device (DMD) based light projector was developed as the target generator in modulation transfer function (MTF) measurement. In order to overcome the sampling-scene phase effect in MTF measurement of sampled imaging systems, a method using random targets is introduced to yield a phase-averaged MTF. The main potential problem of implementing this method is the fact that the stationary assumption of the random targets may be vitiated in practical measurement, especially in field test due to the ill condition. We provide an efficient model-independent way of analyzing and isolating the spectral contents arising from these additional contributions to MTF measurement. Algorithms with adaptive parameter selection were also developed for spectral estimation of the test image in order to overcome the challenge brought by the size limit of the test matrices for one certain field of view derived from the isoplantic region. The MTF measurement of a CCD video imager is used to demonstrate the measurement technique and illustrate the benefits over other methods. In order to validate the results, comparisons have been made between MTF measurements of imager implemented using this method and bar target direct measurements.

Keywords: modulation transfer function, sampling imaging, electro-optical testing , field testing

1. INTRODUCTION

The modulation transfer function （MTF） is an objective metric to quantify the ability of an electro-optical imaging

system to capture fine detail found in the original scene. It is determined by a number of factors, including the performance of the camera lens as well as the detector technology and the electrical circuits in the camera, which may include electronic processing and storage of the imagery. The spatial sampling process of an electro-optical system commonly leads to non-isoplantic effects, thus violates the spatial-invariant characteristic, which the traditional MTF theory is based on. Wittenstein1, Park2, and et al. extend the definition of isoplanatism to the frequency domain, and a concept of phase-averaged MTF obtained over a statistical ensemble of stimuli positions was developed. Techniques commonly used to measure MTF, such as knife-edge targets and slanted slit targets, which can be generally called deterministic targets, negate the sampling process and inherently set the sampling MTF to 1 at all frequencies. This leads to a discrepancy between measuring results of MTF and the real performance of the system. Other methods, including bar and sinusoidal targets as well as slit target, depend on the alignment of the targets and the sampling sites, with best alignment giving the broadest MTF. Compare with other MTF measurement techniques, the method using random targets has several proven advantages. The best known advantage is that it includes the MTF due to the sampling of the image3, thus it may provide a more accurate prediction of the imaging system performance in the field. It is also estimated to be suitable for both complete system MTF measuring and components of the system, such as the

5th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment, edited by Yudong Zhang, Jose M. Sasian, Libin Xiang, Sandy To,

Proc. of SPIE Vol. 7656, 76565I · © 2010 SPIE · CCC code: 0277-786X/10/$18 · doi: 10.1117/12.866223

Proc. of SPIE Vol. 7656 76565I-1

Downloaded From: http://proceedings.spiedigitallibrary.org/ on 04/16/2013 Terms of Use: http://spiedl.org/terms

lens .Random targets were created using both laser speckle4,5 and transparency3 based technology, or just displayed on an ordinary computer screen6 before.

In this study we concentrated on measuring the MTF of the sampled imaging system in field test. To provide a more flexible and spectrally neutral test pattern, we developed a digital mirror device (DMD) based light projector to display the random targets, which was estimated to have a good performance to resist the surround of high reflectance and flare light in field. The stationary assumption of the random targets is often erupted in practice and thus invalidates the method. We discussed this problem and provide an algorithm to cover the issue, which was never addressed before as the best we know. We also developed an adaptive spectral estimation algorithm to get a more accurate MTF measuring result.

2. SYSTEM DESCRIPTION 2.1 Design of Test Pattern

A pseudorandom test matrix drawn from a uniform distribution on the unit interval was created using the Ziggurat algorithm by Marsaglia7. This method can generate uniformly distributed double-precision values over the interval [2^(-53), 1-2^(-53)].In order to avoid the display limitation of linearity and increase the frame rates of DMD, we convert gray-level random targets to binary random targets(0 or 1). This binary matrix has essentially the same PSD as the gray-level matrix. Figure 1(a) shows a segment of the binary random targets we created. The power spectral density (PSD) of the original matrix projected along one axis is shown in Figure 1(b), with a linear vertical scale normalized from 0 to 1. We get the estimation of PSD using the algorithm described below.

Figure.1（a）Segment of binary random targets,(b) PSD of original matrix projected along one axis.

The test matrix is upload into DMD memory through the DVI interface and assign the “ON” condition to the mirror pixels responding to the binary value “1” (“OFF” to the binary value “0” ), then projected to the unit under test (UUT), creating a two-dimensional radiance pattern. This sets an optical stimuli with a band-limited constant spatial power spectrum, ( )inPSD ξ , over the band[0, maxξ ] for the system, where maxξ is the maximum spatial frequency. Figure 2 is a schematic of the setup we used to measure MTF.

(b) (a)



Figure 2 Schematic of the setup used to measure MTF.

The first step in measuring MTF is to capture an image of the target with the camera under test. The camera’s analog output is captured and sampled by the frame grabber and stored in the memory for the following process executed in the software. According to Nyquist-Shannon sampling theorem, the magnification of the test matrix can be adjusted to obtain a ratio of target pixel to image pixel of 1:1, where the maximum frequency is got, which is approximately the Nyquist frequency. The output power spectral density, ( )outPSD ξ , is then estimated .The input and output PSDs are related in the following manner:

2( ) ( ) ( )out inPSD H PSDξ ξ ξ= (1)

where ( )H ξ is the system transfer function or MTF of the system.

2.2 DMD based target projector

We use the Texas Instruments Discovery 1100 series 0.7′′ XGA DDR device in our setup. Its core part is an XGA format (1024×768) micromirror array with a 13.68µm pitch size and a 12°± tilt angle. Each mirror is independently controlled by loading data into the memory cell below the mirror to steer reflected light, spatially mapping a pixel of video data to a pixel on a display.

The projector optical system consists of an illumination system and a projection system. By using the total-internal-reflectance (TIR) prism, the illumination is separated from the projection path, and these systems can be treated independently. High uniformity was achieved using the combines of hollow rod integrator and relay optics assembly. This kind of illuminating technique is commonly used on DMD products today8, however, to support electrical-optic test, the projection system has many different design considerations than the standard projector applications where the image is projected onto a screen.

The output of the projector is usually collimated at an infinite conjugate. The exit pupil must have sufficient relief and size to over-fill the entrance pupil of the UUT, and meet the requirement of no vignetting at the edges of the field, to

Integrator Rod

Fold Mirror

CCD Camera

Lamp Relay Optics

DMD

TIR Prism

Projection Lens

Computer

Translation Stage

Frame Grabber



avoid infiltration of unwanted external radiation into the UUT. The effective focal length and the size of the DMD determine the projector’s FOV. It is usually challenging to simultaneously meet the projector’s FOV and pupil diameter requirements while maintaining resolving power and pupil uniformity. The final design is a balance of performance, cost, size and other system parameters. A 200 mm f/4 projector with a 50 mm pupil diameter and a 50 mm relief was built. The optical performance was optimized to be close to the diffraction limit over the whole FOV at the visible waveband. The solid model of the projection optics and the ray tracing are shown in Figure 3.

Figure.3 Solid model of projection optics and ray tracing.

The target projector is designed to withstand severe field conditions, also be compact and lightweight for easier transportation. The projector optical assemble and DMD drive electronics are enclosed in a robust mechanical envelope, which prevents accidental misalignments and breakage, temperature drifts and stray light.

2.3 MTF measuring algorithm

MTF measurement of electro-optical imaging systems is actually a system identification problem, where the imaging system is taken as a stable, linear, time-invariant, and causal filter. The random targets method estimates the filter parameters by analyzing the steady-state frequency response of the unknown system to white noise inputs. In practical applications, the output sequence is often a colored sequence, as color is introduced by the filter, with time-varying bias and nonstationary noise covariance, the stationary assumption of the estimating process is often vitiated, especially in field test. This is due to the commonly existing imaging system defects, such as optical system cosn θ effect, f θ− effect, etc. even in the so called aberration free system, not to mention the various kinds of unavoidable measurement noise, include image motion and vibration, atmospheric turbulence, and aerosol scattering, just to mention a few, which introduce a broad-band spectral contents with unknown amplitudes.

In general, the high frequencies of a signal influence the details, while the low frequencies influence the associated approximations. To overcome the nonstationary issue, an algorithm was developed by first splitting the signal components, and applying soft thresholding to the detail coefficients of each level, then a wide-sense stationary signal can be extracted form the origin signal by reconstructing the processed coefficients of levels from 1 to J . To simplify analysis, only one dimension is considered here. The rationale supports two dimensions instances too.

We apply wavelet transform to the output signal ( )f x , in the basis of functions φ and ψ with usual notations9, J



being an integer, ( )f x can be denoted as

, , , ,( )J

J k J k j k j kk j k

f x a dφ ψ=−∞

= +∑ ∑ ∑ (2)

We know the definition of the coefficients:

, , ( ) ( )J k J ka x f x dxφ= ∫ (3)

And similarly

, , ( ) ( )J k J kd x f x dxψ= ∫ (4)

With a finite set of n observations, it is possible to estimate only a finite set of coefficients, those belonging to the levels

from 1 to J , and to some positions k . Approximations are moved out from ( )f x , which act as the time-varying bias.

The values ,j kd , lower than a threshold t , are set to 0 in a hard thresholding manner. The threshold is decided mainly

by the noise levels near Nyquist frequency, where noise is often a dominating contribution to the signal.

{ },, , , ,

1

( ) 1j k

J

J k J k j k j kd tk j k

s x a dφ ψ>

=

= +∑ ∑∑ (5)

The result, ( )s x , is quite satisfactory, not only by the statistical criterion, but also on a visual perception point of view.

The images before and after the process are shown in Figure 4.

Figure.4(a) Original captured image, (b) Image after process.

Images are now prepared for spectral analysis, however, problems remain that estimating the PSD function ( )φ ω of a

signal from a finite number of observations N is ill posed from a statistical standpoint, unless we make some appropriate assumptions on ( )φ ω . Let ( )s x be an AR process of order p . The estimation of ( )φ ω is reduced to the linear prediction problem. Then ( )s x satisfies

(a) (b)



1( ) ( ) ( ) ( ) ( )

pT

kk

e x s x a s x k s x xϕ θ=

= + − = +∑ (6)

Where [ ]( ) ( 1), , ( ) Tx s x s x pϕ = − −L . We interpret ( )e x as the corresponding prediction error. The vector θ that

minimizes the prediction error variance { }2 2( )n E e xσ = is the AR coefficient vector. An AR model is built as

1( ) 1

pjw jwk

kk

A e a e− −

=

= +∑ (7)

We filter ( )s x by θ to form ( )e x , Then estimate the signal PSD ( )φ ω as

2

ˆ ( )ˆ( )ˆ( )

m iwkek mr k e

wA w

φ−

=−= ∑ (8)

where ˆ( )r k are the standard ACS estimates for ( )e x . The filter is used to smooth the ( )φ ω , and reduces statistical

variability of the signal periodogram, precise model dimension selection and parameters estimation of the filter are not important here, because all structure errors remain in the final results.

Assume we have estimated the PSD of both the input and output images, the MTF can be calculated according to equation 1.The final MTF was got by removing the test set MTF from the results, the details is beyond the discuss here, which can be found in reference 3,6.

3 SYSTEM VALIDATION AND EXAMPLES OF MEASUREMENTS

3.1 System validation

To validate the test set we built, we measured the MTF of a CCD video camera. The results were compared with that from a 4-bar target direct measurement, as there is no world recognized standard MTF system known to us, and the MTF derived from PSF (point spread function) or other Fourier transfer based methods may be inconclusive to the correctness of our results because of the complex data processing. For an infinite square wave, we define the contrast transfer function (CTF) as the image modulation depth as a function of spatial frequency. We then derive a MTF curve using the composition of a series of CTF functions.

Before we carried out the experiment, the test was modeled with computer simulations just to validate the algorithm alone. We use a built-in image simulation function of the optical design software Zemax to simulate the imaging process of a lens, by setting the pixel size and the grid sampling format to use in the pupil space, the detector is also involved in the formation of image. We estimate the MTF using simulated image of a random target bitmap and the presented algorithm, the MTF result is compared with the prediction by Zemax. In figure 5 good agreement between the Zemax prediction and the simulation measurement results is shown within a ± 4% error bar. This shows validation of the



algorithm to a certain extent. We examined the performance of the whole system in field test, where the benefit of our system over others really lies, as will show below.

Figure.5 Simulated MTF results.

3.2 Examples of measurements

Measurement was made for a Sony XC-ES30 industrial black-and-white video camera module, using a 1/3-inch IT CCD. The sensor’s peak response is for light with wavelength near 500 nm, with greater than 50% relative response from 410 to 680 nm. The CCD active area has 768 (H)×494(V) pixels with cell size 6.35(H)×7.4(V) mμ .The camera operates in frame integration mode in which vertically adjacent pixels are not integrated, with γ correction off and gain mode

selected to manual gain.

A 50-mm lens with f/1.8 was used with the camera module for the measurement. The CCD camera with lens was aligned directly in front of the DMD projector, as has been depicted in Fig.2, at a distance of approximately 5 cm. Strict alignment are not as demanding as that needed in other methods, because the DMD projector works at an infinite conjugate, and the inner immunity of the algorithm to phase effect.

The analog video signal from the CCD camera was captured with a frame-grabber board. A total of 24-bit quantization is obtained for RGB acquisition. The result is a 768 (H)×576 (V) digital image. Each subsequent image pixel represents approximately a 6.35× 6.35 mμ square area of the 4.8 mm×3.6 mm sensor. The frame grabber uses a DH-VT120

single-chip front-end video decoder for processing of the analog video signal.

A bitmap of the test matrix with 300×300 target pixels was generated with a personal computer and sent to the DMD projector. Spatial resolution must be changed to meet the spectral boundary requirement of the test. We do this change simply by combining several DMD mirrors into one effective pixel. As the combined magnification of the projector and imager is 0.25, each target pixel was represented with 2×2 pixels on the DMD and imaged to one image pixel in the frame-grabbed output, yielded a 6.84 mμ image pixel in the image plane. Thus the maximal frequency reaches to 73.10 /lp mm , a litter smaller than the Nyquist frequency, 78.74 /lp mm , meets the test requirement.



The experimental results for the tangential MTF and sagittal MTF are shown in Fig. 6(a) and 6(b) compared with that from the 4-bar target method. There is an excellent match between the two sets of results. The 4-bar target was carefully oriented parallel to the columns or rows of the CCD array and was moved randomly in plane, the MTF was calculated by averaging 10 CTF-derived MTF curves.

Figure 6(a) Tangential MTF measurement results, (b) Sagittal MTF measurement results.

The results show that better than 3% precision is achievable using the sample matrix size of about 300*300. The total

number of samples in each dimension of the sample matrix doesn’t need to be 2 p (p an integer) in our algorithm, as is

(a)

(b)



again a typical requirement in before mentioned work, thus improves the flexibility of such method. The repeatability of the test set was measured by dynamically changing the test matrix using the DMD projector and comparing the results. The variation in MTF was less than 2%.

4. CONCLUSIONS

A new method and instrument setup for MTF measurement in field test is proposed. We have shown the basic design principles of the DMD projector and demonstrated its advantages as a target generator. We analyzed factors affecting the validity of random target method in practical applications, and described in detail the processing algorithm. The experiments and results described in this study show that MTF measuring of sampled imaging systems in field test with high precision and repetitiveness is achieved. The most important advantages of the system include relaxed alignment tolerances, flexible target generating, robust environment shielding and easy transportation.

REFERENCES

1. W. Wittenstein, J. C. Fontanella, A. R. Newbery and J. Baars, The definition of the OTF and the measurement of aliasing for sampled imaging systems, Opt. Acta. 29(1), 41–50 (1982). 2. S. K. Park, R. Schowengerdt and M. A. Kaczynski, Modulation-transfer-function analysis for sampled image systems, Appl. Opt. 23(15), 2572–2582 (1984). 3. A. Daniels, G. D. Boreman, A. D. Ducharme, and E. Sapir, Random transparency targets for modulation transfer function measurement in the visible and infrared regions, Opt. Eng. 34(3), 860–868 (1995). 4. A. D. Ducharme and S. P. Temple, Improved aperture for modulation transfer function measurement of detector arrays beyond the Nyquist frequency, Opt. Eng. 47(9) (2008) 5. A. M. Pozo, A. Ferrero, M. Rubino, J. Campos and A. Pons, Improvements for determining the modulation transfer function of charge-coupled devices by the speckle method, Opt. Express 14(13),5928–5936(2006) 6. E. Levy, D. Peles, M. O. Lipson, S. G. Lipson, Modulation transfer function of a lens measured with a random target method, Appl. Opt. 38(4),679–683(1999) 7. G. Marsaglia and W. W. Tsang, The ziggurat method for generating random variables, Journal of Statistical Software 5(8) (2000) 8. J. W. Bowron and R. P. Jonas, Off-axis illumination design for DMD systems, Proc. of SPIE Vol. 5186, 72-82 (2003) 9. O. Rioul and M. Vetterli, Wavelets and signal processing, IEEE Signal Processing Magazine, 1991



Date post:	09-Dec-2016
Category:	Documents
Upload:	sandy
View:	212 times
Download:	0 times

SPIE Proceedings [SPIE 5th International Symposium on Advanced Optical Manufacturing and Testing...

Documents