Extending the depth of field with chromatic aberration for dual-wavelength iris imaging.

We propose a method of extending the depth of field to twice that achievable by conventional lenses for the purpose of a low cost iris recognition front-facing camera in mobile phones. By introducing intrinsic primary chromatic aberration in the lens, the depth of field is doubled by means of dual wavelength illumination. The lens parameters (radius of curvature, optical power) can be found analytically by using paraxial raytracing. The effective range of distances covered increases with dispersion of the glass chosen and with larger distance for the near object point.

Numerical modeling of spatial coherence using the elementary function method.

The elementary function method is an approximate method for propagation calculations in spatially, partially coherent light in two dimensions. In this paper, we present the numerical application of this method to a 248 nm UV excimer laser source. We present experimental results of the measurement of the degree of spatial coherence and the beam profile of this source. The elementary function method is then applied to the real beam data and used to simulate the effects of imaging an opaque edge with a source of varying degrees of spatial coherence. The effect of spatial coherence on beam homogenization is also presented.

Improved fixation quality provided by a Bessel beacon in an adaptive optics system.

PURPOSE: We investigate whether a structured probe beam that creates the beacon for use in a retinal imaging adaptive optics system can provide useful side effects. In particular we investigate whether a Bessel beam that is seen by the subject as a set of concentric rings has a dampening effect on fixation variations of the subject under observation. This calming effect would allow longer periods of observation, particularly for patients with abnormal fixation. METHOD: An experimental adaptive optics system developed for retinal imaging is used to monitor the fluctuations in aberrations for artificial and human subjects. The probe beam is alternated between a traditional beacon and one provided by a Bessel beam created by SLM. RESULTS: Time-frequency analysis is used to indicate the differences in power and time variation during fixation depending on whether the Bessel beam or the traditional beacon is employed. Comparison is made with the response for an artificial eye to discount systemic variations. CONCLUSION: Significant evidence is accrued to indicate the reduced fluctuations in fixation when the Bessel beam is employed to create the beacon.

Backscattering measurements from double-scale randomly rough surfaces.

We present experimental measurements of light backscattered from double-scale randomly rough surfaces (oceanlike surfaces) with different statistical parameters illuminated at small and large angles of incidence. The surfaces are composed of a small-scale roughness superimposed on a slowly (large-scale) varying surface. The large-scale surfaces are diamond-machined periodic surfaces made on aluminum substrates and have either a sinusoidal or a Stokes wave profile. The small-scale roughness is added with lithographic techniques, and the surfaces are then gold coated. For a linearly polarized incident beam, it is found that the backscattered light is strongly depolarized mainly at small angles of incidence and strong shadowing effects are present for large angles of incidence (θ(inc) > 60°).

Singular-value decomposition of a tomosynthesis system.

Tomosynthesis is an emerging technique with potential to replace mammography, since it gives 3D information at a relatively small increase in dose and cost. We present an analytical singular-value decomposition of a tomosynthesis system, which provides the measurement component of any given object. The method is demonstrated on an example object. The measurement component can be used as a reconstruction of the object, and can also be utilized in future observer studies of tomosynthesis image quality.

Reconstruction of the optical system of the human eye with reverse ray-tracing.

We present a practical method for reconstructing the optical system of the human eye from off-axis wavefront measurements. A retinal beacon formed at different locations on the retina allows probing the optical structure of the eye by the outgoing beams that exit the eye through the dilated pupil. A Shack-Hartmann aberrometer measures the amount of wave aberrations in each beam at the exit pupil plane. Wavefront data obtained at different oblique directions is used for tomographic reconstruction by optimizing a generic eye model with reverse ray-tracing. The multi-configuration system is constructed by tracing pre-aberrated beams backwards from each direction through the exit pupil into the optical system of the aberrometer followed by the generic eye model. Matching all wave aberrations measured at each field point is equivalent to minimizing the size of the beacon spots on the retina. The main benefit of having a personalized eye model is the ability to identify the origin of the ocular aberrations and to find the optimal way for their correction.

Atmospheric dispersion compensation for extremely large telescopes.

Achieving diffraction limited imaging with future ground-based optical telescopes will require adaptive optics for correction of atmospheric turbulence and also efficient techniques for atmospheric dispersion compensation. We study the benefit of using a linear atmospheric dispersion corrector (ADC) coupled with a deformable mirror on a 42-m Extremely Large Telescope (ELT) operating in the VIRJ spectral bands. The ADC design consists of two identical thin wedges made of F5 glass. The amount of dispersion introduced by the ADC is adjusted by translating one of the wedges along the optical axis so that it always cancels atmospheric dispersion as it varies with telescope elevation. We show that the ADC working in conjunction with a deformable mirror provides diffraction-limited image quality over a 1-arcmin field.

Population study of the variation in monochromatic aberrations of the normal human eye over the central visual field.

We present data analysis for ocular aberrations of 60 normal eyes measured with a Hartmann-Shack (HS) wavefront sensor (WFS). Aberration measurements were made on-axis and at 5 degree field angles in the nasal, inferior, temporal and superior semi-meridians. Particular attention is given to aberration distributions and possible strategies for aberration correction are discussed. A versatile HS WFS was designed and constructed with features of simultaneous pupil centre determination, off-axis capability, real-time data displays, and efficient lenslet sampling orientation. The subject alignment is achieved by the use of a parallel channel that is recombined with the sensing channel to simultaneously image the eye and the HS spots onto a single CCD. The pupil centre is determined using this image of the eye (iris edge), rather than the HS spots. The optical design includes a square lenslet array positioned with its diagonals aligned with the most typical principal astigmatic meridians of the eye. This favourable orientation helps to enlarge the dynamic range of the WFS. The telecentric re-imaging of the HS spots increases the robustness of the system to defocus in the event of CCD misalignment.

Linearity of the pyramid wavefront sensor.

The pyramid wavefront sensor is very similar to the Fourier knife-edge test, but employs dynamic modulation to quantify the phase derivative. For circular modulation, we compare approximate geometrical optics calculations, more exact diffraction calculations, and experimental results. We show that both the sinusoidal and the approximate linear relationship between wavefront derivative and wavefront sensor response can be derived rigorously from diffraction theory. We also show that geometrical, diffraction and experimental results are very similar, and conclude that the approximate geometrical predictions can be used in place of the more complex diffraction results.

Study of the tear topography dynamics using a lateral shearing interferometer.

The dynamics of the pre-corneal tear film topography are studied on 21 subjects with a purpose-built lateral shearing interferometer. Interesting tear topography features such as post-blink undulation, break-up, eyelid-produced bumps/ridges, bubbles and rough pre-contact lens tear surfaces were recorded. Using the calculated tear topography maps, the effects of the tear dynamics in visual performance, refractive surgery and ophthalmic adaptive optics are discussed in terms of wavefront RMS. The potential of lateral shearing interferometry for clinical applications such as dry eye diagnosis and contact lens performance studies is illustrated by the recorded topography features such as post-blink undulation, break-up, eyelid-produced bumps/ridges, bubbles and rough tear surfaces in front of contact lenses.

Elementary functions: propagation of partially coherent light.

The theory of propagation of partially coherent light is well known, but performing numerical calculations still presents a difficulty because of the dimensionality of the problem. We propose using a recently introduced method based on the use of elementary functions [Wald et al. Proc. SPIE6040, 59621G (2005)] to reduce the integrals to two dimensions. We formalize the method, describe its inherent assumptions and approximations, and introduce a sampling criterion for adequate interpolation. We present an analysis of some special cases, such as the Gaussian Schell-model beam, and briefly discuss generalized numerical propagation of two-dimensional field distributions.

Systematic design of an anastigmatic lens axicon.

We present an analytical method for systematic optical design of a double-pass axicon that shows almost no astigmatism in oblique illumination compared to a conventional linear axicon. The anastigmatic axicon is a singlet lens with nearly concentric spherical surfaces applied in double pass, making it possible to form a long narrow focal line of uniform width. The front and the back surfaces have reflective coatings in the central and annular zones, respectively, to provide the double pass. Our design method finds the radii of curvatures and axial thickness of the lens for a given angle between the exiting rays and the optical axis. It also finds the optimal position of the reflecting zones for minimal vignetting. This method is based on ray tracing of the real rays at the marginal heights of the aperture and therefore is superior to any paraxial method. We illustrate the efficiency of the method by designing a test axicon with optical parameters used for a prototype axicon, which was manufactured and experimentally tested. We compare the optical characteristics of our test axicon with those of the experimental prototype.

Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions.

Maximum-likelihood (ML) estimation in wavefront sensing requires careful attention to all noise sources and all factors that influence the sensor data. We present detailed probability density functions for the output of the image detector in a wavefront sensor, conditional not only on wavefront parameters but also on various nuisance parameters. Practical ways of dealing with nuisance parameters are described, and final expressions for likelihoods and Fisher information matrices are derived. The theory is illustrated by discussing Shack-Hartmann sensors, and computational requirements are discussed. Simulation results show that ML estimation can significantly increase the dynamic range of a Shack-Hartmann sensor with four detectors and that it can reduce the residual wavefront error when compared with traditional methods.

Lens axicons in oblique illumination.

Lens axicons, i.e., lenses or lens systems designed to work like axicons, can be a simple and inexpensive way of generating the characteristic axicon focal line. In the design of most lens axicons, only on-axis properties have been considered. We present the design of a lens axicon with improved off-axis characteristics. It is constructed from a singlet lens but with a double-pass feature that allows for a line of uniform width and a stop positioned to minimize aberrations. We perform off-axis analysis and experiments for this system and for another lens axicon, one designed for its on-axis characteristics. We conclude that the off-axis performance of the double-pass axicon is better than both that of an ordinary cone axicon and that of the other lens axicon.

Objective assessment of image quality. IV. Application to adaptive optics.

The methodology of objective assessment, which defines image quality in terms of the performance of specific observers on specific tasks of interest, is extended to temporal sequences of images with random point spread functions and applied to adaptive imaging in astronomy. The tasks considered include both detection and estimation, and the observers are the optimal linear discriminant (Hotelling observer) and the optimal linear estimator (Wiener). A general theory of first- and second-order spatiotemporal statistics in adaptive optics is developed. It is shown that the covariance matrix can be rigorously decomposed into three terms representing the effect of measurement noise, random point spread function, and random nature of the astronomical scene. Figures of merit are developed, and computational methods are discussed.

Singular-value decomposition for through-focus imaging systems.

Singular-value decomposition (SVD) of a linear imaging system gives information on the null and measurement components of object and image and provides a method for object reconstruction from image data. We apply SVD to through-focus imaging systems that produce several two-dimensional images of a three-dimensional object. Analytical expressions for the singular functions are derived in the geometrical approximation for a telecentric, laterally shift-invariant system linear in intensity. The modes are evaluated numerically, and their accuracy confirmed. Similarly, the modes are derived and evaluated for a continuous image representing the limit of a large number of image planes.

Coherence function analysis of the higher-order aberrations of the human eye.

We measured the wavefront aberrations of the eyes of five subjects with a Shack-Hartmann sensor sampling at 21.2 Hz and decomposed the measurements into Zernike aberration terms up to and including the fifth radial order. Coherence function analysis was used to determine the common frequency components between the aberrations within subjects. We found the results to be highly subject dependent. The coherence values were typically <0.4. Possible reasons for this are discussed. Coherence function analysis is a useful tool that can be used in future investigations to determine correlations between the aberration dynamics of the eye and other physiological mechanisms.

Adaptive optics system for investigation of the effect of the aberration dynamics of the human eye on steady-state accommodation control.

It is now known that defocus is not the only aberration in the eye that exhibits dynamic behavior during fixation. It is currently unknown what effects, if any, the dynamics of these other aberrations have on steady-state accommodation control. We constructed an adaptive optics system to serve as a tool for future investigations in this area. The system has several design features of interest, including automated precompensation of defocus and astigmatism and a method to bypass a scanner used to reduce speckle. It also has the facility to measure the eye's aberrations independent of the aberration manipulation device-a 37-actuator membrane deformable mirror. Coherence function analysis was used to assess the deformable mirror performance in terms of coupling between Zernike modes. Modes beyond third radial order showed severe coupling. Pilot data were collected on one subject to demonstrate the utility of this system in steady-state accommodation studies. The value of the system for future work in this area is discussed.

Double lateral shearing interferometer for the quantitative measurement of tear film topography.

A lateral shearing interferometer designed and built for the study of the precorneal tear film topography dynamics and its effect on visual performance is presented. Simple data processing algorithms are discussed and tested on data illustrating different tear topography features: postblink tear undulation, tear breakup, eyelid-produced bumps and ridges, bubbles, and rough precontact lens tear surfaces.

Weak correlation between the aberration dynamics of the human eye and the cardiopulmonary system.

It is fairly well established that the higher-order aberrations of the eye fluctuate over relatively short time periods, but as yet there is no conclusive evidence regarding the origin of these fluctuations. We measured the aberrations and the pulse pressure wave simultaneously for five subjects. The aberrations were measured by using a Shack-Hartmann sensor sampling at 21.2 Hz. We decomposed the aberration data into Zernike coefficients up to and including fifth order and also calculated the rms wave-front error. From the pulse data the heart rate variability signal was also derived. Coherence function analysis showed that for all subjects there was a weak correlation between many of the aberrations and the pulse and the derived heart rate variability. The pulse and the heart rate variability can account for only 11% +/- 2% and 20% +/- 2%, respectively, of the aberration dynamics.