Pupil Shape Research Articles

Binary-Shaped Pupil Coronagraphs for High-Contrast Imaging Using a Space Telescope with Central Obstructions

Abstract We present sets of configurations of binary-shaped pupil coronagraphs optimized for a realistic space telescope to directly detect extrasolar giant planets. For the purpose of mid-infrared observations, the target contrast ratio is set to $10^{-7}$. We made a systematic assessment of the performance of two recently proposed pupil shapes, “checkerboard” and “concentric ring” masks, where a large central obstruction due to a secondary mirror and its related support spiders was introduced into the telescope pupil. It turned out that, if the secondary mirror diameter is smaller than $\sim 15 \%$ of the diameter of the primary, the checkerboard-type masks are more promising in terms of the total high-contrast area. With such a small secondary, we propose to modify the original symmetrical checkerboard apodization function. This modification enables us to achieve a $10^{-7}$ contrast at an inner working angle (IWA) of $4.0 \,\lambda/D$. On the other hand, when the secondary mirror size cannot be reduced to that level, the concentric ring masks are preferable because of their larger transmission. It was also found that the transmission through the optimal binary masks exhibits two characteristic features as the IWA increases: firstly, abrupt increases and secondly, plateaus. We attribute this nature of the binary apodization functions to the existence of threshold IWAs that allow large openings in the pupil.

Evaluation of Pupil Dynamics After Implantation of Artisan Phakic Intraocular Lenses

To compare pre- and postoperative horizontal and vertical pupil diameters after horizontal Artisan phakic intraocular lens (PIOL) (Ophtec BV, Groningen, The Netherlands) implantation for correction of myopia. The pre- and postoperative scotopic pupil diameters measured by the Colvard pupillometer (Oasis Medical, Glendora, Calif) were compared in 71 eyes after Artisan PIOL implantation (Artisan Colvard group). Analysis of pupil shape (vertical vs horizontal diameter, V/H ratio) after horizontal Artisan PIOL implantation was performed with the Procyon pupillometer (Procyon Instruments Ltd, London, United Kingdom) in 121 eyes (Artisan Procyon group) under scotopic, mesopic-low, and mesopic-high conditions and compared to an age- and refraction-matched control group of 121 eyes of refractive surgery candidates (Procyon control group). After horizontal Artisan PIOL implantation, the mean horizontal pupil diameter decreased from 6.231 +/- 0.70 mm preoperatively to 5.34 +/- 0.68 mm postoperatively in the Artisan Colvard group (P < .01). The mean horizontal scotopic diameter was 5.60 +/- 0.66 mm, the mesopic-low diameter was 4.94 +/- 0.71 mm, and the mesopic-high diameter was 3.98 +/- 0.54 mm for the Artisan Procyon group. The mean horizontal scotopic diameter was 6.29 +/- 0.91 mm, the mesopic-low diameter was 5.40 +/- 0.96 mm, and the mesopic-high diameter was 4.16 +/- 0.80 mm in the Procyon control group. A significant increase was noted in V/H ratio under scotopic, mesopic-low, and mesopic-high conditions from 1.02, 1.02, and 1.01, respectively, in the Procyon control group to 1.17, 1.12, and 1.06, respectively, in the Artisan Procyon group (P < .01). Horizontal pupil size was significantly decreased after horizontal Artisan PIOL implantation and might be attributed to a mechanical restriction of the iris in the horizontal meridian.

Visual Optics: The Shapes of Pupils

The eyes of many terrestrial vertebrates have slit-shaped pupils. A new hypothesis links this pupil shape to the way that vertebrate lenses compensate for chromatic aberration.

Pupil shapes and lens optics in the eyes of terrestrial vertebrates

Animal eyes that are primarily used under low-light conditions usually have optical systems of short depth of focus, such that chromatic defocus may lead to considerable blurring of the images. In some vertebrates, the problem is solved by multifocal lenses having concentric zones of different focal lengths, each of which focuses a different relevant spectral range onto the retina. A partially constricted circular pupil would shade the peripheral zones of the lens, leading to the loss of well-focused images at relevant wavelengths. The slit pupil, however, allows for use of the full diameter of the lens even in bright light. We studied species of terrestrial vertebrates from a variety of phylogenetic groups to establish how widespread multifocal lenses are and how pupil shapes are adapted to the optical systems. We found that multifocal lenses are common from amphibians to mammals, including primates. Slit pupils were only present in animals having multifocal optical systems. Among the felids, small species have multifocal lenses and slit pupils, while large species have monofocal lenses and round pupils. The Eurasian lynx, a cat of intermediate size, has an intermediate eye design. The functional significance of the absence of multifocal optical systems in large felids remains mysterious, because such systems are present in other large-eyed terrestrial vertebrates. Multifocal optical systems in nocturnal prosimians suggest that those animals have colour vision despite being described as cone monochromats.

Pupil phase apodization for imaging of faint companions in prescribed regions

We consider the ‘faint companion’ problem where substantial reduction of diffraction sidelobes is required in order to image a faint neighbour near a much brighter source. In addition to well-known pupil amplitude and shape apodization methods, we found that the required sidelobe reduction can be obtained by appropriate spatial phase modulations over an aperture. Here, our previous results on one-sided phase apodization in astronomical applications are extended in several ways. Specifically, (i) round and square pupil cases are examined via a simple computational approach based on Fourier iterations; (ii) finite target regions are considered in the image plane; (iii) the discrete (square pupil) phase functions are used to construct a segmented mirror. The mirror provides sidelobe reduction sufficient for imaging of extrasolar planets.

Iterative zonal wave-front estimation algorithm for optical testing with general-shaped pupils

An iterative zonal wave-front estimation algorithm for slope or gradient-type data in optical testing acquired with regular or irregular pupil shapes is presented. In the mathematical model proposed, the optical surface, or wave-front shape estimation, which may have any pupil shape or size, shares a predefined wave-front estimation matrix that we establish. Owing to the finite pupil of the instrument, the challenge of wave front shape estimation in optical testing lies in large part in how to properly handle boundary conditions. The solution we propose is an efficient iterative process based on Gerchberg-type iterations. The proposed method is validated with data collected from a 15 x 15-grid Shack-Hartmann sensor built at the Nanjing Astronomical Instruments Research Center in China. Results show that the rms deviation error of the estimated wave front from the original wave front is less than lambda/130-lambda/150 after approximately 12 iterations and less than lambda/100 (both for lambda = 632.8 nm) after as few as four iterations. Also, a theoretical analysis of algorithm complexity and error propagation is presented.

Colobomas of the Iris in a Flock of Rosecomb Bantam Chickens

A defect in the pupil shape ofrosecomb bantam chickens was noticed by a breeder. The pupil in affected birds appeared to be elongated at the lower margin and consistent with a coloboma of the iris. Upon examination of all birds in the flock, the defect was found in 26% of females and 9% of males. Examination of breeders older than 1 yr led to the discovery ofcolobomas, although there were not enough birds to accurately determine the prevalence of the problem for previous generations. Affected birds were examined for other lesions, and none were found. Specific-pathogen-free (SPF) eggs were incubated and hatched with eggs from the affected flock as sentinels. No SPF chicks developed colobomas of the iris, while 37% of the bantams in the same hatch were affected. This experiment eliminated many possible infectious agents and incubator or brooder malfunction as causes of this eye lesion. An analysis of the flock pedigree suggested that the defect might be inherited and might be related either to feather color or to gender. No statistically significant correlation could be made between feather color and the iris colobomas. However, the trait was twice as likely to occur in females as in males, which suggests that it is a sex-influenced trait. Based on the determination that this was an inherited trait, a breeding strategy to reduce the prevalence of the lesion in which affected birds were removed from the breeding flock was developed and followed for 2 yr. The prevalence of colobomas was 22% in females and 2.9% in males after the first year and 7.8% and 0.8% in females and males, respectively, after the second year.

후면 위상 패턴을 이용한 투과율 조절 포토마스크

후면의 석영면에 위상 패턴을 형성하여 투과율 조절을 구현한 포토마스크에 대해 보고한다. 위상 패턴의 크기와 패턴 조밀도에 따른 조명 동공의 형태 변화에 관한 이론적 결과와 투과율 조절 포토마스크를 사용한 웨이퍼 상 CD(critical dimension) 균일도 개선에 관한 실험적 결과에 대해 기술한다. 투과율 조절을 위한 위상 패턴은 패턴이 형성되지 않은 영역에 대해 180<TEX>$^{\circ}$</TEX>의 상대적 위상을 갖도록 석영면을 식각한 콘택홀 형태의 패턴을 사용하였다. 콘택홀 패턴의 크기가 작을수록 본래의 조명동공 형태를 유지하게 되며, 동일한 패턴 조밀도에서 더욱 큰 노광 광세기 저하가 일어남을 알 수 있었다. 패턴 조밀도를 위치별로 변화시켜 CD균일도 개선에 적합한 투과율 분포를 포토마스크 후면에 형성하였다. 투과율 조절 포토마스크를 140nm 디자인 롤을 갖고 있는 DRAM(Dynamic Random Access Memory)의 한 주요 레이어에 적용하여 CD 균일도를 3<TEX>$\sigma$</TEX>값으로 24.0nm에서 10.7nm 로 개선할 수 있었다. We report on a transmittance controlled photomask with phase patterns on the back quartz surface. Theoretical analysis for changes in illumination pupil shape with respect to the variation of size and density of backside phase patterns and experimental results for improvement of critical dimension uniformity on a wafer by using the transmittance controlled photomask are presented. As phase patterns for controlling transmittance of the photomask we used etched contact-hole type patterns with 180" rotative phase with respect to the unetched region. It is shown that pattern size on the backside of the photomask must be made as small as possible in order to keep the illumination pupil shape as close as possible to the original pupil shape and to achieve as large an illumination intensity drop as possible at a same pattern density. The distribution of illumination intensity drop suitable for correcting critical dimension error was realized by controlling pattern density of the contact-hole type phase patterns. We applied this transmittance controlled photomask to a critical layer of DRAM (Dynamic Random Access Memory) having a 140nm design rule and could achieve improvement of the critical dimension uniformity value from 24.0 nm to 10.7 nm in 3<TEX>$\sigma$</TEX>.TEX>.

An optical/UV space coronagraph concept for the terrestrial planet finder

NASA’s current strategic plan calls for the launching of a space observatory, The Terrestrial Planet Finder (TPF), by the middle of the next decade; it will search for terrestrial planets in the habitable zone of roughly 150 nearby stars and characterize them for the potential to harbor life. This paper describes a visible light concept for TPF developed by the Ball Aerospace led TPF study team. This concept consists of a 4 m by 10 m coronagraphic telescope in a deep space orbit. Imaging planets requires overcoming the problem of high contrast between the light from the parent star and from the planet, coupled with their small angular separation. For a coronagraph, the diffraction pattern of the telescope must be suppressed at the planet image location. The high contrast needed can be achieved using optimized pupil shapes that provide the needed 10 billion times suppression as close as 4 λ/ D to the center of the star. In addition, wavefront errors induced by the mirror deformities will be corrected using deformable mirrors in a novel active optics system that corrects both amplitude and phase errors. The paper describes the baseline design of a visible light telescope and instrument that will meet the mission requirements.

Extrasolar Planet Finding via Optimal Apodized‐Pupil and Shaped‐Pupil Coronagraphs

In this paper we examine several different apodization approaches to achieving high-contrast imaging of extrasolar planets and compare different designs on a selection of performance metrics. These approaches are characterized by their use of the pupil's transmission function to focus the starlight rather than by masking the star in the image plane as in a classical coronagraph. There are two broad classes of pupil coronagraphs examined in this paper: apodized pupils with spatially varying transmission functions and shaped pupils, whose transmission values are either 0 or 1. The latter are much easier to manufacture to the needed tolerances. In addition to comparing existing approaches, numerical optimization is used to design new pupil shapes. These new designs can achieve nearly as high a throughput as the best apodized pupils and perform significantly better than the apodized square aperture design. The new shaped pupils enable searches of 50%-100% of the detectable region, suppress the star's light to below 10-10 of its peak value, and have inner working distances as small as 2.8λ/D. Pupils are shown for terrestrial planet discovery using square, rectangular, circular, and elliptical apertures. A mask targeted at Jovian planet discovery is also presented, in which contrast is given up to yield greater throughput.

A Coronagraph with a Band‐limited Mask for Finding Terrestrial Planets

Several recent designs for planet-finding telescopes use coronagraphs operating at visible wavelengths to suppress starlight along the telescope's optical axis while transmitting any off-axis light from circumstellar material. We describe a class of graded coronagraphic image masks that can, in principle, provide perfect elimination of on-axis light, while simultaneously maximizing the Lyot stop throughput and angular resolution. These band-limited masks operate on the intensity of light in the image plane, not the phase. They can work with almost any entrance pupil shape, provided that the entrance pupil transmissivity is uniform, and can be combined with an apodized Lyot stop to reduce the sensitivity of the coronagraph to imperfections in the image mask. We discuss some practical limitations on the dynamic range of coronagraphs in the context of a space-based terrestrial-planet finder telescope and emphasize that fundamentally, the optical problem of imaging planets around nearby stars is a matter of precision fabrication and control, not Fraunhofer diffraction theory.

Reduction of the edge effects induced by the boundary of a linear-carrier interferogram

There are a great variety of techniques used to obtain the wrapped phase of a carrier frequency interferogram. We are interested in interferograms whose data points lie in bounded region data. Analysis of this kind of interferogram with the Fourier or synchronous method contains an important source of error at its edge. In this paper we propose a new method that reduces this boundary error effect. This method consists of an iterative technique to obtain a very good estimate of the phase of a carrier frequency interferogram bounded by an arbitrary pupil's shape. We suggest a method in order to reduce the boundary effects at the edge by giving a first phase estimation obtained by the Fourier or synchronous method.

Misalignment of flexible iris hook retractors for small pupil cataract surgery: effects on pupil circumference

A graphical method was used to assess the effect on pupil shape and circumference of various flexible iris hook malpositions. Results confirmed that all hook malpositions necessitate increased pupil stretching to create space to perform a capsulorhexis of a given diameter. This method also confirmed that the addition of a fifth hook to create a pentagonal pupil reduces pupil stretching by 17%. A simple method of marking the limbus before hook insertion to ensure equidistant hook separation and thus minimize pupil stretching is suggested.

Iterative method to obtain the wrapped phase in an interferogram with a linear carrier

There is a great variety of techniques used to obtain the wrapped phase of a carrier frequency interferogram. We are interested in interferograms that have a bounded region data. Analyses of this kind of interferograms with the Fourier or synchronous method have an important source of error at the edge of the interferogram. In this paper we propose a new method that works out this boundary error effect. We describe an iterative synchronous method to obtain a very good phase estimation of a carrier frequency interferogram bounded by an arbitrary pupil's shape. We also show that the proposed iterative method has a continuous and stable convergence towards the true modulating phase of the interferogram.

Generalized wave-front reconstruction algorithm applied in a Shack–Hartmann test

A generalized numerical wave-front reconstruction method is proposed that is suitable for diversified irregular pupil shapes of optical systems to be measured. That is, to make a generalized and regular normal equation set, the test domain is extended to a regular square shape. The compatibility of this method is discussed in detail, and efficient algorithms (such as the Cholesky method) for solving this normal equation set are given. In addition, the authors give strict analyses of not only the error propagation in the wave-front estimate but also of the discretization errors of this domain extension algorithm. Finally, some application examples are given to demonstrate this algorithm.

Multifocal lenses compensate for chromatic defocus in vertebrate eyes

The focal length of the vertebrate eye is a function of wavelength, i.e. the eye suffers from longitudinal chromatic aberration. Chromatic defocus is a particularly severe problem in eyes with high light-gathering ability, since depth of field is small due to a pupillary opening that is large in relation to the focal length of the eye. Calculations show that in such eyes only a narrow spectral band of light can be in focus on the retina. For the major part of the visual spectrum, spatial resolution should be limited by the optics of the eye and far lower than the resolving power achievable by the retinal cone photoreceptor mosaic. To solve this problem, fishes with irises unresponsive to light have developed lenses with multiple focal lengths. Well-focused images are created at the wavelengths of maximum absorbance of all spectral cone types. Multifocal lenses also appear to be present in some terrestrial species. In eyes with mobile irises, multifocal lenses are correlated with pupil shapes that allow all zones of the lens, with different refractive powers, to participate in the imaging process, irrespective of the state of pupil constriction.

Long-term follow-up of primary anterior chamber intraocular lens implantation

Purpose: To evaluate the long-term outcome in eyes having primary anterior chamber intraocular lens (AC IOL) implantation.Setting: Kimura Eye and Internal Medicine Hospital, Hiroshima, Japan.Methods: Primary AC IOL implantation was performed in 171 eyes from 1983 to 1988. Two lenses were implanted: the open C-loop Simcoe lens and the 4-point fixation Kelman lens. In 86 eyes that had a mean follow-up of 9 years 7 months, visual acuity, corneal endothelial cell density, pupil shape, and the presence of associated complications were examined.Results: Although the final visual acuity was 0.5 or better in 60 eyes (69%), corneal endothelial cell density was less than 2000 cells/mm2 in 46 eyes (57%). Postoperative complications included a deformed pupil in 48 eyes (56%) and bullous keratopathy in 12 eyes (14%). In 14 eyes the AC IOL was explanted; 11 of these were the open C-loop Simcoe lens.Conclusion: Although our findings show that the open C-loop AC IOL (Simcoe) is contraindicated, implantation of the 4-point fixation AC IOL may be acceptable in selected cases.

Small incision single-suture-loop pupilloplasty for postoperative atonic pupil

In this small incision technique to correct postoperative atonic pupil in the aphakic or pseudophakic eye, the pupil is sutured and constricted with a 10-0 polypropylene loop through 3 1.0 mm stab incisions. The surgery is easier to perform than previous methods, appears safe and reproducible, and requires little special equipment. Although the pupil's shape may become slightly irregular, its size is fairly easy to regulate. This new method should be useful in correcting postoperative atonic pupil, and the small incision technique will likely minimize surgical trauma and induced astigmatism.

'D-shaped' and 'reverse-D-shaped' pupil in a cat with lymphosarcoma.

A 7-year-old female spayed European shorthair cat was presented because of visual reduction and a green reflex in the right eye. Examination revealed a 'D-shaped' pupil in the right eye and a 'reverse-D-shaped' pupil in the left eye. Both eyes showed fibrinous anterior uveitis with exudates in the anterior chamber and precipitates on the posterior surface of the cornea. In both eyes a chorioretinitis was diagnosed which caused partial retinal detachment and peripapillary oedema in the left eye. Histopathology revealed intestinal and ocular lymphosarcoma. The aberrant pupil shapes which persisted after death were due to infiltration of the iris stroma and were not caused neurologically. The observation that in both eyes only the medial parts of the iris were affected could not be explained.

Effect of postoperative mydriatics on the iris

Purpose: To assess the role postoperative mydriatics play after extracapsular cataract extraction (ECCE) and posterior chamber intraocular lens (IOL) implantation in causing iris modifications and in controlling inflammation.Setting: Outpatients Department, Ninewells Hospital, Dundee, Scotland.Methods: The prospective study comprised 136 patients who had standardized ECCE. Half the patients used a mydriatic for 2 weeks postoperatively. Anterior chamber activity, pain, and eye redness were evaluated at 2 weeks postoperatively; pupil shape, peripheral anterior synechias, IOL position, and iris adhesions, at 6 weeks.Results: Iris-lens adhesions were significantly more common in the group using a mydriatic. There was no difference between the two groups in postoperative inflammation.Conclusion: Mydriatics should not be used routinely after ECCE with posterior chamber IOL implantation.