1. Binarization of gray-scale hologram Fan Jiang Fall 2006

2. Introduction Optics Diffraction theory and hologram Motivation Approach Simple threshold Random binarization High-frequency binarizaion Result comparison (The whole project is done on Mathematica)

3. Optics diffraction theory and hologram Optics diffraction theory-Fraunhofer diffraction- Fourier Transform Hologram-can be used to reconstruct the target object. Target object hologram Reconstruction image binarization Gray-scalebinary Gray-scale

4. Motivation Computer-generated holograms are widely used today. However, during the lithography, we can only write binary holograms on the mask. Binarize the gray-scale hologram is important!

5. Approach 1 Want to change a gray scale to binary? - Threshold! Threshold = Median [hologram data] Histogram of the gray-scale hologram Binary hologram

6. Approach 2 Random Binarization Create n (n< total pixel number) pseudorandom number as the address of data, and use the median number for these data as the threshold, then binary these part of numbers. Repeat this process until all the numbers become 0 or 1. Process Gray-scale hologram Binarize n random pixels All the pixels are binarized? Binary hologram Yes No

7. Approach 2 Binarization Result: The change of histogram: Binary hologram:

8. Approach 3 High-frequency binarization In this method, threshold is still needed. Median [hologram data] is chosen as the threshold. But after using threshold, pick up the max. intensity under the threshold, and set it to 1. Similarly, pick up the min. intensity above the threshold, set it to 0. So, all the peaks are set to be 1, all the valleys are set to be 0, independent on the threshold. ----- almost all the high frequency information has been saved.

9. Approach 3 Example in 1-D: Binary hologram:

10. Results Now compare the reconstructions of the three binary holograms. Gray-scale Method 1 Method 2 Method 3

11. Results We can also compare the mean-square error of the results. Gray-scale: 0.01 Method 1: 1.021 Method 2: 1.019 Method 3: 0.81

12. Conclusion As the result shown above. In my case, high- frequency binarization method is the best one among the three of them. But all of them are much worse than the result of gray-scale. Better binarization method is still needed! – Future work.