Deconvolution Theory

Cells and tissues are three-dimensional structures, so the observed image at the focal plane contains not only information from the plane on which the microscope is focused, but also "out-of-focus" contributions from other parts of the specimen above and below the plane of focus. This complicates the interpretation of the 3D structure of the biological specimen in optical imaging. The image at a given focal plane is a poor estimate of a true section through the thick specimen. To remedy these problems and produce mere reliable 3D data, the most widely techniques are digital deconvolution and confocal microscopy. A confocal microscope uses the pinhole aperture to restrict the "out-of-focus" flare reaching a single detector, the photomultiplier tube (PMT). Because of the pinhole aperture, all the fluorescence signal collected by the objective lens is not used. In order to increase the signal, increased excitation laser intensity is used, but this will often introduce photobleaching and photodamage.

Unlike the confocal configuration, digital deconvolution microscopy uses all of the fluorescence signal collected by the objective lens without using pinhole to deliver the emitted light to 2D high-sensitivity and linear CCD detectors. The "out-of-focus" flare introduced into the imaging at different optical sections is reversed by computer deconvolution through the use of a pointspread function (PSF) of the imaging system.

Deconvolution is the procedure which reverses the image degradation due to convolution (i.e., inverse Fourier transform.) By modeling the microscope optics as a linear and shift-invariant system, the PSF can be used to describe the transformation of any image by the microscope. A typical fluorescence microscope image can be

[measured image] = [PSF] * [desired image] 
where '*' symbol represents the mathematical operation of convolution. The deconvolution (*-1), the mathematical inverse of convolution can be represented as

[desired image] = [measured image] (*-1) [PSF] 
The goal of deconvolution is to solve the equation for the desired image.

Deconvolution improves the resolution of the image acquired at different focal planes to localize or visualize the proteins or molecular structure of the biological specimen in three-dimension. Deconvolution requires very intensive computer operation to process the images in a reasonable amount of time. A powerful workstation with large hard disk space and memory should allow images to be processed within reasonable time compared to the personal computers which require an array processor sub-system to speed up the deconvolution.