Computational Optics

Optical imaging has evolved far beyond simply looking at the images captured by the camera. The amount of information that can be extracted from the images captured by our setups can be maximized by harnessing the computational techniques on the images post-acquisition. Researchers have utilized both mathematical models of image formation and advances in artificial intelligence and machine learning to not only enhance the quality of images captured, but also to automate the translation these images to meaningful biological information.

In this section, we describe the various computational techniques to not only enhance the resolution and the overall quality of OCT images but also methods to maximize the information discerned from them. We describe the scattering problem in optical coherence tomography and how interferometric synthetic aperture microscopy restores focal-plane resolution across the entire volume. 

Computational dispersion correction and k-space resampling in OCT  

Dispersion compensation

k-space resampling

Beam-divergence, scattering, and aberrations

Figure 2.2.  Illustration for the effect of OCT system’s NA on the expected OCT images. Each row corresponds to a specific numerical aperture of the system from very low NA (≈0), low NA (≈0-0.2), and high NA (> 0.5). The OCT images shown in the right column are not actual images but are cartoon illustrations. The axes are as indicated in the image. 

Figure 2.3. Zernike Polynomials from orders N =0 to 6. Polynomials in a row have the same order N. Commonly observed aberrations such as defocus, astigmatism, and spherical are indicated. 

Wavefront sampling and forward problem

Wavefront sampling

Image formation in OCT

Description in space domain

Description in spatial-frequency domain

Approximations for a practical system

Adding aberrations to the model

Summary of the forward problem

Inverse problem

Solving the scattering problem the traditional way

Solving the inverse scattering problem with resampling

Practical considerations

Algorithm for ISAM and CAO

Results from just wavefront resampling and aberration correction