binarization of gray-scale hologram fan jiang fall 2006
TRANSCRIPT
![Page 1: Binarization of gray-scale hologram Fan Jiang Fall 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649ed55503460f94be5a6b/html5/thumbnails/1.jpg)
Binarization of gray-scale hologram
Fan Jiang
Fall 2006
![Page 2: Binarization of gray-scale hologram Fan Jiang Fall 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649ed55503460f94be5a6b/html5/thumbnails/2.jpg)
Introduction
Optics Diffraction theory and hologram Motivation Approach Simple threshold Random binarization High-frequency binarizaion Result comparison
(The whole project is done on Mathematica)
![Page 3: Binarization of gray-scale hologram Fan Jiang Fall 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649ed55503460f94be5a6b/html5/thumbnails/3.jpg)
Optics diffraction theory and hologram
Optics diffraction theory-Fraunhofer diffraction-Fourier Transform
Hologram-can be used to reconstruct the target object.
Target object hologram hologram
Reconstruction image
binarization
Gray-scale binary
0 10 20 30 40 50 60
0
10
20
30
40
50
60
0 10 20 30 40 50 60
0
10
20
30
40
50
60
Gray-scale
0 10 20 30 40 50 60
0
10
20
30
40
50
60
![Page 4: Binarization of gray-scale hologram Fan Jiang Fall 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649ed55503460f94be5a6b/html5/thumbnails/4.jpg)
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!
![Page 5: Binarization of gray-scale hologram Fan Jiang Fall 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649ed55503460f94be5a6b/html5/thumbnails/5.jpg)
Approach 1
Want to change a gray scale to binary? - Threshold!
Threshold = Median [hologram data]Histogram of the gray-scale hologram
Binary hologram
2 4 6 8
2000
4000
6000
8000
10000
12000
0 10 20 30 40 50 60
0
10
20
30
40
50
60
![Page 6: Binarization of gray-scale hologram Fan Jiang Fall 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649ed55503460f94be5a6b/html5/thumbnails/6.jpg)
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
![Page 7: Binarization of gray-scale hologram Fan Jiang Fall 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649ed55503460f94be5a6b/html5/thumbnails/7.jpg)
Approach 2
Binarization Result:The change of histogram:
Binary hologram:
1 2 3 4
2500
5000
7500
10000
12500
15000
17500
1 2 3 4
2500
5000
7500
10000
12500
15000
17500
1 2 3 4
5000
10000
15000
20000
1 2 3 4
5000
10000
15000
20000
1 2 3 4
5000
10000
15000
20000
1 2 3 4
5000
10000
15000
20000
25000
1 2 3 4
5000
10000
15000
20000
25000
1 2 3 4
5000
10000
15000
20000
25000
1 2 3 4
5000
10000
15000
20000
25000
1 2 3 4
5000
10000
15000
20000
25000
30000
1 2 3 4
5000
10000
15000
20000
25000
30000
1 2 3 4
5000
10000
15000
20000
25000
30000
1 2 3 4
5000
10000
15000
20000
25000
30000
1 2 3 4
5000
10000
15000
20000
25000
30000
1 2 3 4
5000
10000
15000
20000
25000
30000
1 2 3 4
5000
10000
15000
20000
25000
30000
1 2 3 4
5000
10000
15000
20000
25000
30000
1 2 3 4
5000
10000
15000
20000
25000
30000
35000
1 2 3 4
5000
10000
15000
20000
25000
30000
35000
1 2 3 4
5000
10000
15000
20000
25000
30000
35000
1 2 3 4
5000
10000
15000
20000
25000
30000
35000
1 2 3 4
5000
10000
15000
20000
25000
30000
35000
1 2 3 4
5000
10000
15000
20000
25000
30000
35000
0.5 1 1.5 2 2.5 3
5000
10000
15000
20000
25000
30000
35000
0.5 1 1.5 2 2.5 3
5000
10000
15000
20000
25000
30000
35000
0.5 1 1.5 2 2.5 3
5000
10000
15000
20000
25000
30000
35000
0.5 1 1.5 2 2.5 3
5000
10000
15000
20000
25000
30000
35000
0.5 1 1.5 2 2.5 3
10000
20000
30000
0.5 1 1.5 2 2.5 3
10000
20000
30000
0.5 1 1.5 2 2.5 3
10000
20000
30000
40000
0.5 1 1.5 2 2.5 3
10000
20000
30000
40000
0.25 0.5 0.75 1 1.25 1.5
500
1000
1500
2000
0.25 0.5 0.75 1 1.25 1.5
500
1000
1500
2000
0.2 0.4 0.6 0.8 1 1.2 1.4
500
1000
1500
2000
0.2 0.4 0.6 0.8 1 1.2 1.4
500
1000
1500
2000
0.2 0.4 0.6 0.8 1 1.2 1.4
500
1000
1500
2000
0.2 0.4 0.6 0.8 1 1.2
500
1000
1500
2000
0.2 0.4 0.6 0.8 1
500
1000
1500
2000
0 10 20 30 40 50 60
0
10
20
30
40
50
60
![Page 8: Binarization of gray-scale hologram Fan Jiang Fall 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649ed55503460f94be5a6b/html5/thumbnails/8.jpg)
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.
![Page 9: Binarization of gray-scale hologram Fan Jiang Fall 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649ed55503460f94be5a6b/html5/thumbnails/9.jpg)
Approach 3 Example in 1-D: Binary hologram:
0 10 20 30 40 50 60
0
10
20
30
40
50
60
![Page 10: Binarization of gray-scale hologram Fan Jiang Fall 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649ed55503460f94be5a6b/html5/thumbnails/10.jpg)
Results Now compare the reconstructions of the three binary
holograms.
Gray-scale Method 1
Method 2 Method 30 10 20 30 40 50 60
0
10
20
30
40
50
60
0 10 20 30 40 50 60
0
10
20
30
40
50
60
0 10 20 30 40 50 60
0
10
20
30
40
50
60
0 10 20 30 40 50 60
0
10
20
30
40
50
60
![Page 11: Binarization of gray-scale hologram Fan Jiang Fall 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649ed55503460f94be5a6b/html5/thumbnails/11.jpg)
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
![Page 12: Binarization of gray-scale hologram Fan Jiang Fall 2006](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649ed55503460f94be5a6b/html5/thumbnails/12.jpg)
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.