Compound prism design principles, II: triplet and Janssen prisms

Abstract

Continuing the work of the first paper in this series [Appl. Opt. 50, 4998–5011 (2011)], we extend our design methods to compound prisms composed of three independent elements. The increased degrees of freedom of these asymmetric prisms allow designers to achieve greatly improved dispersion linearity. They also, however, require a more careful tailoring of the merit function to achieve design targets, and so we present several new operands for manipulating the compound prisms’ design algorithm. We show that with asymmetric triplet prisms, one can linearize the angular dispersion such that the spectral sampling rate varies by no more than 4% across the entire visible spectral range. Doing this, however, requires large prisms and causes beam compression. By adding a beam compression penalty to the merit function, we show that one can compromise between dispersion linearity and beam compression in order to produce practical systems. For prisms that do not deviate the beam, we show that Janssen prisms provide a form that maintains the degrees of freedom of the triplet and that are capable of up to 32° of dispersion across the visible spectral range. Finally, in order to showcase some of the design flexibility of three-element prisms, we also show how to design for higher-order spectral dispersion to create a two-dimensional spectrum.

Multimodal single-molecule microscopy with continuously controlled spectral resolution

“…Furthermore, the nonlinear dispersion of the prisms created varying spectral resolution across the spectrum, forcing different RPA for the same spectral resolution in different wavelengths. This will be improved in future work by carefully designing the prism material and apex angles ( 58 ). Another limitation for spectral analysis with the current CoCoS system arises in cases in which only a single-color channel is detected per PSF.…”

Multi-octave high-dynamic range optical spectrometer for single-pulse diagnostic applications

“…A comprehensive description of the optimization criteria can be found in Refs. [41][42][43]. A global optimization algorithm based on the differential evolution method was employed in order to determine the prism geometry for a series of available infrared materials.…”

Compound prism design principles, I

“…and T. Dereniak, on the other hand, take advantage of theory developed for superachromat lenses [30,31] to give explicit expressions for the first-order design of compound nondeviating prisms with linearized dispersion ([32]), allowing one to see the explicit dependence on the mean index, Abbe V -number, and partial dispersion of the glasses used in the design. (See Section 4 below, and also Section 2 of Paper II [17]. ) An early book that appears to contain relevant material, but which has proven inaccessible to us, is Ref.…”