Axicons have been proposed for imaging applications since they offer the advantage of extended depth of field (DOF). This enhanced DOF comes at the cost of degraded image quality. Image processing has been proposed to improve the image quality. Initial efforts were focused on the use of an axicon in a borescope thereby extending depth of focus and eliminating the need for a focusing mechanism. Though promising, it is clear that image processing would lead to improved image quality. This would also eliminate the need, in certain applications, for a fiber optic imaging bundle as many modern day video borescopes use an imaging sensor coupled directly to the front end optics.

In the present work, three types of refractive axicons are examined:​ a linear axicon, a logarithmic axicon and a Fresnel axicon. The linear axicon offers the advantage of simplicity and a significant amount of scientific literature including the application of image restoration techniques. The Fresnel axicon has the advantage of compactness and potential low cost of production. As no physical prior examples of the Fresnel axicons were available for experimentation until recently, very little literature exists. The logarithmic axicon has the advantage of nearly constant longitudinal intensity distribution and an aspheric design producing superior pre-processed images over the aforementioned elements. Point Spread Functions (PSFs) for each of these axicons have been measured. These PSFs form the basis for the design of digital image restoration filters. The performance of these three optical elements and a number of restoration techniques are demonstrated and compared.