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Electronic Imaging & Signal Processing

Increasing image resolution using a deformable mirror

Combining a deformable mirror with a super-resolution algorithm enables higher-resolution images from a relatively simple system.
22 January 2007, SPIE Newsroom. DOI: 10.1117/2.1200701.0561

Obtaining high-resolution imagery is very important in many areas, such as medical imaging and industrial inspection. CCD arrays with small pixels can provide good resolution, but if the pixel is too small, the signal will fluctuate due to the quantized nature of photons. Another way to improve resolution while fixing the field of view is to increase both the magnification over the optical system as well as the whole size of the detector. However, designing an optical system free of aberration for the entire large field is usually difficult and expensive.

Super-resolution is a well-known technique that constructs a higher-resolution image from multiple low-resolution images.1 Some researchers have tried to increase image resolution using a translating mirror2 or liquid-crystal spatial light modulator (LC-SLM)3 to obtain multiple, slightly different observations, and then use these with the super-resolution algorithm. Yet mounting a mirror on a translational stage limits the use of the mirror to this specific application, while the image-shifting method using LC-SLM suffers from several problems, such as chromatic aberration and high-order diffracted rays.

Using a deformable mirror to shift the image position has several advantages compared with the other methods mentioned above. First, the quality of the image reflected by the continuous mirror surface is better than the image formed by the pixelated LC-SLM. Second, using a deformable mirror instead of a translation stage makes the system more compact. Finally, the deformable mirror approach is more versatile because it is applicable to other tasks, for example, focusing or dynamic aberration correction. We obtained four regularly shifted images using this system and constructed a high-resolution image using a super-resolution algorithm.

In the experimental setup, a 15mm, 37-channel electrostatically driven micromachined membrane deformable mirror (MMDM) is placed in the conjugate position to the aperture stop as shown in Figure 1. Four slightly different images of the object are obtained by changing the shape of the mirror's surface and processing these images using Deepu Rajan's super-resolution algorithm,4 which employs an optimization method to synthesize a high-resolution image from blurred, noisy, low-resolution images.

Figure 1. A deformable mirror modulates the input beam, and an iris determines the effective radius of the deformable mirror.

We used a US Air Force resolution target as an object for testing our method (see Figure 2). To compare the super-resolution result with the real image taken by the camera, we set the virtual sensor resolution at half of the original one, i.e., we integrated four neighboring pixels to form a new pixel. Figure 3 shows the real image of the specified area, and Figure 4 shows four different observations of reduced size.

Figure 2. A US Air Force resolution target used as the object in the experiment.

Figure 3. Real image of the specified area.

Figure 4. Reduced observations: four neighboring pixels in the real image (shown in Figure 3) are integrated to make each virtual pixel. Each observation is obtained with a different mirror shape.

The experimental result is shown in Figure 5 together with a bilinearly interpolated image of one of the observations. The result seems even clearer than the ideal (unreduced) image shown in Figure 3 due to the restoration effect of the super-resolution algorithm. To see the pure super-resolution effect, we restored the bilinearly interpolated image. The result is presented in Figure 6. The significant difference appears at the first element of the fifth group, and the sixth element of the fourth group, which are indicated by the arrows. In both regions, the three lines are resolved in the super-resolved image, but not in the simply restored image.

Figure 5. Results of two methods of increasing resolution. (a) Superresolution image obtained from the observations in Figure 4. (b) A bilinearly interpolated image.

Figure 6. Comparison with the simply restored image: simple restoration can make the image look clearer but does not increase the resolution, as indicated by the arrows.

In summary, we set up an active imaging system whose pupil function can be modulated by a deformable mirror. We demonstrated super-resolution experimentally. The benefit of using a deformable mirror in the pupil plane is that this same optical system can also be used for applications such as aberration correction and dynamic focusing, applications that normally use deformable mirrors. In the future, we intend to implement this super-resolution method with the other functionalities using the same optical setup.

Deokhwa Hong and Hyungsuck Cho
Mechanical Engineering, Korea Advanced Institute of Science and Technology
Daejeon, South Korea

Deokhwa Hong graduated from the Mechanical and Aerospace Engineering Department of Seoul National University in 2005 and is currently studying for a PhD in the Mechanical Engineering Department of Korea Advanced University. His research interest is in machine vision and metrology.

Hyungsuck Cho received his BS degree from Seoul National University in 1971, his MS degree from Northwestern University in 1973, and his PhD degree from the University in 1973, and his PhD degree from the University of California at Berkeley in 1977. Since 1978, he has been a professor with Department of Production Engineering,Department of Automation and Design, Seoul Campus, and is currently with the Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST). In addition, he was the founding chair of the SPIE Opto-Mechatronic Systems conference in 2000 and has chaired or co-chaired the conference since 2006. He has written numerous papers for this and other SPIE conferences.