Point Spread Function (PSF) design to shape the focal field distribution of an optical system is very important to many applications: optical microscopy, lithography, optical tweezers, etc. However, often this design process includes tedious numerical calculations and complex optimisation procedures.
In this paper, we explain to the readers the benefits of the well-established Extended Nijboer-Zernike theory(a most recent updates of the ENZ theory can be found in https://www.jeos.org/index.php/jeos_rp/article/view/13044/1026 ) :
- The 3-D focal field distribution of each Zernike mode on the exit pupil can be analytically obtained and the contribution of each mode to the total focal field are solely related by its Zernike coefficient;
- The Zernike modes(polynomials ) form a complete and orthogonal set on a unit circle.
Based on these merits, we developed an optimisation algorithm to find a focal field with extended depth of focus. Since the focal fields of Zernike modes are analytically obtained, our optimization parameters are reduced to the number of Zernike modes applied.
We have build up an experimental setup to demonstrate this idea: a Spatial Light Modulator(SLM) is used to shape the pupil field and a scanning stage is used to measure the 3D focal intensity distribution.
And the actual measurements validated our theoretical results:
Ref.:
A. P. Konijnenberg, L. Wei, N. Kumar, L. C. C. P. Filho, and H. P. Urbach. Demonstration of an optimised focal field with long focal depth and high transmission obtained with the extended nijboer-zernike theory. Opt. Express, 22(1):311–324, Jan 2014.
