1. Description
This experiment is designed to sharpen a set of images taken in sequence in a set of focal planes. A discrete Fourier transform is applied to the stack of images, using an estimated point spread function (psf) as a basis for deconvolution.
2. Methods
To test this technique, onion cells were stained with methylene blue and images through a microscope at 400X magnification were taken by digital camera. These 7 images were decimated to a 300-by-300 matrix, representing standard grayscale images. The results are based on this set of sample images, and use of MATLAB to perform Fourier transforms and spectral division. Since this process starts with 256 grayscale images, some amount of error due to image quantization is expected. Operations are carried out using double-precision floating point to minimize this source of error.
The pixel intensity is stored in a 300X300X7 matrix, allowing techniques to be applied to any layer of the matrix, or applied to several layers simultaneously. Since the first and last images are at the focal extremes of the process, and the Fourier methods will treat the focal sequence as circular, little improvement is expected in those images. Although several psf distributions were attempted, if was found that using psf values which diminish rapidly (on the order of 1/e per layer-squared) tended to yield less severe ringing and spectral artifacts.
The chosen PSF (cascaded into one image) and its Fourier transform at +/- one layer are shown:
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3. Results
Before attempting deconvolution, a simple averaging of the 7 images was used to show the cells being imaged and what the spectrum looks like:
| (YZ) | Image Average (XY) | Magnitude Spectrum |
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(XZ) |
The first and last images were omitted, since the deconvolution provided little change to those out-of-focus images. Five of the 7 images, and their transformed results are shown:
| Layer | Original Image | Transformed Image |
| 2nd Image |  |
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| 3rd Image |  |
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| 4th Image |  |
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| 5th Image |  |
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| 6th Image |  |
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4. Conclusions
The effect of this technique, along with careful selection of point spread function, tends to reduce the blurring between imaged focal planes. This can result in a better analysis of microscopic detail by isolating features to the plane being visualized.
