Hybrid FPGA-CPU pupil tracker.

An off-axis monocular pupil tracker designed for eventual integration in ophthalmoscopes for eye movement stabilization is described and demonstrated. The instrument consists of light-emitting diodes, a camera, a field-programmable gate array (FPGA) and a central processing unit (CPU). The raw camera image undergoes background subtraction, field-flattening, 1-dimensional low-pass filtering, thresholding and robust pupil edge detection on an FPGA pixel stream, followed by least-squares fitting of the pupil edge pixel coordinates to an ellipse in the CPU. Experimental data suggest that the proposed algorithms require raw images with a minimum of ∼32 gray levels to achieve sub-pixel pupil center accuracy. Tests with two different cameras operating at 575, 1250 and 5400 frames per second trained on a model pupil achieved 0.5-1.5 µm pupil center estimation precision with 0.6-2.1 ms combined image download, FPGA and CPU processing latency. Pupil tracking data from a fixating human subject show that the tracker operation only requires the adjustment of a single parameter, namely an image intensity threshold. The latency of the proposed pupil tracker is limited by camera download time (latency) and sensitivity (precision).

Centroid error due to non-uniform lenslet illumination in the Shack-Hartmann wavefront sensor.

Images formed by individual Shack-Hartmann wavefront sensor lenslets are displaced proportionally to the average wavefront slope over their aperture. This principle fails when the lenslet illumination is non-uniform. Here we demonstrate that the resulting error is proportional to the linear component of the illumination intensity, the quadratic wavefront component, and the lenslet size. For illustrative purposes, we compare the error due to centered Gaussian illumination decaying by 30% at the pupil edge against the error due to assuming the wavefront at the lenslet center being equal to the wavefront average across each lenslet. When testing up to ninth-order Zernike polynomial wavefronts and simulating nine lenslets across the pupil, the maximum centroid errors due to non-uniform illumination and sampling are 1.4% and 21%, respectively, and 0.5% and 6.7% when considering 25 lenslets across the pupil in the absence of other sources of error.

Design of two spherical mirror unobscured relay telescopes using nodal aberration theory.

Nodal aberration theory is used to calculate the third-order aberrations that result in image blur for an unobscured modified 4f relay (2f1 + 2f2) formed by two tilted spherical mirrors for objects at infinity (infinite conjugate) and near the front focal plane of the first mirror (finite conjugate). The field-averaged wavefront variance containing only non-rotationally symmetric aberration coefficients is then proposed as an optimization metric. Analytical and ray tracing optimization are demonstrated through sample designs. The particular cases of in-plane and orthogonal folding of the optical axis ray are discussed, followed by an analysis of a modified 2f1 + 2f2 relay in which the distance of the first mirror to the object or pupil is allowed to vary for aberration correction. The sensitivity of the infinite conjugate 2f1 + 2f2 relay to the input marginal ray angle is also examined. Finally, the optimization of multiple conjugate systems through a weighted combination of wavefront variances is proposed.

Long eye relief fundus camera and fixation target with partial correction of ocular longitudinal chromatic aberration.

A combined 32° full field of view refractive fundus camera and fixation target with a -20 to +10 diopter sphere correction range is described and demonstrated. The optical setup partially corrects the average longitudinal chromatic aberration and spherical aberration of the human eye, while providing a long eye relief to allow integration with reflective adaptive optics ophthalmoscopes, as a viewfinder. The fundus camera operates with 940 nm light, using a maximum 2.9 mm diameter imaging pupil at the eye. The fixation target uses a light projector capable of delivering red, green and/or blue spatially and temporally modulated stimuli to the retina. The design and performance of each sub-system are discussed, and retinal imaging at various wavelengths is demonstrated.

An effective solvent theory connecting the underlying mechanisms of osmolytes and denaturants for protein stability.

An all-atom Go model of Trp-cage protein is simulated using discontinuous molecular dynamics in an explicit minimal solvent, using a single, contact-based interaction energy between protein and solvent particles. An effective denaturant or osmolyte solution can be constructed by making the interaction energy attractive or repulsive. A statistical mechanical equivalence is demonstrated between this effective solvent model and models in which proteins are immersed in solutions consisting of water and osmolytes or denaturants. Analysis of these studies yields the following conclusions: 1), Osmolytes impart extra stability to the protein by reducing the entropy of the unfolded state. 2), Unfolded states in the presence of osmolyte are more collapsed than in water. 3), The folding transition in osmolyte solutions tends to be less cooperative than in water, as determined by the ratio of van 't Hoff to calorimetric enthalpy changes. The decrease in cooperativity arises from an increase in native structure in the unfolded state, and thus a lower thermodynamic barrier at the transition midpoint. 4), Weak denaturants were observed to destabilize small proteins not by lowering the unfolded enthalpy, but primarily by swelling the unfolded state and raising its entropy. However, adding a strong denaturant destabilizes proteins enthalpically. 5), The folding transition in denaturant-containing solutions is more cooperative than in water. 6), Transfer to a concentrated osmolyte solution with purely hard-sphere steric repulsion significantly stabilizes the protein, due to excluded volume interactions not present in the canonical Tanford transfer model. 7), Although a solution with hard-sphere interactions adds a solvation barrier to native contacts, the folding is nevertheless less cooperative for reasons 1-3 above, because a hard-sphere solvent acts as a protecting osmolyte.