Efficient and robust recurrence relations for the Zernike circle polynomials and their derivatives in Cartesian coordinates.

For some time it has been known and recommended that the calculation of Zernike polynomials to radial orders higher than 8 to 10 should be performed using recurrence relations rather than explicit expressions due increasingly large cancellation errors. This paper presents a set of simple recurrence relations that can be used for the unit-normalized Zernike polynomials in polar coordinates and easily adapted to Cartesian coordinates as well. The recurrence relations are also well suited for the calculation of the Cartesian derivatives of the Zernike polynomials.

Angularly symmetric splitting of a light beam upon reflection and refraction at an air-dielectric plane boundary: comment.

In a recent paper, conditions for achieving equal and opposite angular deflections of a light beam by reflection and refraction at an interface between air and a dielectric were determined [J. Opt. Soc.

Accurate calculation of diffraction-limited encircled and ensquared energy.

Mathematical properties of the encircled and ensquared energy functions for the diffraction-limited point-spread function (PSF) are presented. These include power series and a set of linear differential equations that facilitate the accurate calculation of these functions. Asymptotic expressions are derived that provide very accurate estimates for the relative amount of energy in the diffraction PSF that fall outside a square or rectangular large detector.

High-order optical aberration coefficients: extension to finite objects and to telecentricity in object space.

We extend the method for the automatic computation of high-order optical aberration coefficients to include (1) a finite object distance and (2) an infinite entrance pupil position (telecentricity in object space). We present coefficients of the power series expansion of the transverse aberration vector with respect to the normalized aperture and field coordinates. Aberration coefficients of very high order (e.

High-affinity small molecule inhibitors of T cell costimulation: compounds for immunotherapy.

Costimulatory molecules are important regulators of T cell activation and thus favored targets for therapeutic manipulation of immune responses. One of the key costimulatory receptors is CD80, which binds the T cell ligands, CD28, and CTLA-4. We describe a set of small compounds that bind with high specificity and low nanomolar affinity to CD80.

Novel CD8+ T cell antagonists based on beta 2-microglobulin.

The CD8 coreceptor of cytotoxic T lymphocytes binds to a conserved region of major histocompatibility complex class I molecules during recognition of peptide-major histocompatibility complex (MHC) class I antigens on the surface of target cells. This event is central to the activation of cytotoxic T lymphocyte (CTL) effector functions. The contribution of the MHC complex class I light chain, beta(2)-microglobulin, to CD8alphaalpha binding is relatively small and is mediated mainly through the lysine residue at position 58.