Point spread function shaping using geometric analysis

Abstract

We present a method for shaping point spread functions (PSF) into simple geometric shapes that are free of noise or speckles. The derived phase distributions are intended for typical 2f setups used for reading out computer generated holograms (CGH). Used in conjunction with existing CGH techniques for spot distributions the shaped PSFs can similarly be distributed on a 3D working volume. The PSF's contiguous intensity and phase make them beneficial in many applications such as photo-stimulation, optical manipulation, multi-photon excitation and laser materials processing. This manuscript presents the derivations of the phase functions and their experimental demonstration.

Three-dimensional light sculpting using a geometric analysis

“…In this work, we sculpt light in 3D using an alternative geometric analysis that takes advantage of the rapid re-configurability of phase-only spatial light modulators. We extend the geometric analysis we have used to derive simplified phase functions for extended two-dimensional shapes [17]. The manuscript mainly discusses the light sculpting methodology, while anticipated applications on optical micromanipulation and microscopy would be done on future investigations.…”

“…An output shape can thus be defined by a collection of constituent points, (x f , y f ). This approach has been successful in generating extended 2D shapes wherein continuous adjacent points (x f , y f ) constitute the output shape [17]. Our geometric mapping thus takes the general form 2The first two terms in Eqn.…”

“…2 that multiply with x f and y f describe the lateral distribution of the output. In some of our examples, we used a line profile as the lateral distribution by encoding a zero-width rectangular point spread function (PSF) [17]. Other known input phase functions that have a direct mapping to the laterally defined output can also be used.…”

“…(7) The above expression results to the following input radius to output axial position mapping. (8) This above form is very similar to what we used to generate a circular PSF [17], except that the output is mapped along a line, and hence the coordinate mapping should be multiplied with a quadratic function. Hence, we arrive at the following phase function: (9) Unlike with the stretched vortex beam, x f and y f can be set as zero for this case.…”

“…Choosing X or x f as the lateral axis, the following phase function forms a line with length L xf at the Fourier plane. (10) Here, A is the length of the input along the X-axis as defined in [17]. Away the focal plane the x f -line beam would normally be diverging along the y f -direction, hence we chose to map input segments along Y into successive z f segments at the output.…”