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A new class of apodizing functions suitable for Fourier spectrometry (and similar applications) is introduced. From this class, three specific functions are discussed in detail, and the resulting instrumental line shapes are compared to numerous others proposed for the same purpose.
Apodization functions with decreasing transmission and their opposite, functions with increasing transmission, are investigated for various central obstruction ratios. The resultant modulation transfer functions are presented for various transmission functions and central obstruction ratios. Conclusions applicable to the improvement of imaging performance are discussed.
Kaiser-Bessel apodization function reduces unwanted sidebands. Report discusses apodization in Fourier-transform spectrometer (FTS) for Advanced Moisture and Temperature Sounder (AMTS). Purpose of apodization in instrument to control shape of spectrum in wavenumber space to keep radiation at other wavelengths in passband of spectrometer out of AMTS wavenumber channel.
The use of a starshade is one technique to perform high contrast imaging with space-based telescopes. The primary function of a starshade is to suppress light from a target star in order to image its orbiting planets. In order to provide the proper apodization function the edges of the starshade must follow a precise in-plane profile. However of equal importance is the issue of light from our own sun scattering off of the edges and entering the telescope. A method to alleviate this problem is to make the edges extremely sharp (< 1 µmterminal radius) such that the area available for scattering is minimized. The combination of these two requirements, along with the need to integrate the edges into a 30-40 m dia. deployable structure, present a number of significant engineering challenges. Substrate etching techniques are used to obtain both the intended profile as well as the edge sharpness. Current efforts implement an isotropic etching process on thin metal substrates. This paper discusses the progress towards producing a sharp optical edge at the coupon level. Samples have been characterized using scanning electron microscopy as well as a custom testbed to assess their scattered-light performance.
Starshades, combined with future space telescopes, provide the ability to detect Earth-like exoplanets in the habitable zone by producing high contrast ratios at small inner working angles. The primary function of a starshade is to suppress light from a target star such that its orbiting planets are revealed. In order to do so, the optical edges of the starshade must maintain their precise in-plane profile to produce the necessary apodization function. However, an equally important consideration is the interaction of these edges with light emanating from our own Sun as scattered and/or diffracted sunlight can significantly degrade the achievable contrast. This paper describes the technical efforts performed to obtain precision, low-scatter optical edges for future starshades. Trades between edge radius (i.e. sharpness) and surface reflectivity have been made and small-scale coupons have been produced using scalable manufacturing processes. A custom scattered light testbed has been developed to quantify the magnitude of scattered light over all sun angles. Models have also been developed to make predictions on the level of reflected and/or diffracted light for various edge architectures. The results of these studies have established a current baseline approach which implements photochemical etching techniques on thin metal foils.
Deep shadowing of a normally incident plane wave by an opaque circular disk is partially negated by the formation of a region of strong intensity surrounding the axis passing normally through the disk center. This local intensity enhancement, historically referred to as the Poisson Spot (also known as the Spot of Arago), has been the principal source of difficulties in applications where a significant reduction of the incident intensity is essential. In particular, the NASA Terrestrial Planet Finder's (TPF) mission requires suppression of direct starlight by at least 10 orders of magnitude over the entire visible spectral range. One technique that has been proposed for blocking the direct starlight is to use a rotationally symmetric disk with petallike segments along its boundary. We find that, even though such configurations could, indeed, theoretically provide the desired intensity reduction, they would require unreasonably small radii of curvature at the petals' tips (in the range of micrometers). When the radii of curvature are increased to 3 mm, the intensity reduction drops to a modest 5 to 6 orders of magnitude. Given that for the NASA's TPF mission the proposed occulter radius would be on the order of 25 m, even the 3 mm radius of curvature would be too small for any practical implementation. Further increases of the radius of curvature result in progressively poorer intensity suppression. As an alternative solution we propose an apodized circular disk. We show that with an optimized apodization function, intensity reductions of at least 10 orders of magnitude can be achieved over the entire visible spectral range. Numerical results are presented for parameters appropriate to the NASA TPF mission.
Reference is made to a study by Tschunko (1979) in which it was discussed how apodization modifies the modulation transfer function for various central obstruction ratios. It is shown here how apodization, together with the central obstruction ratio, modifies the point spread function, which is the basic element for the comparison of imaging performance and for the derivation of energy integrals and other functions. At high apodization levels and lower central obstruction (less than 0.1), new extended radial zones are formed in the outer part of the central ring groups. These transmutation of the image functions are of more than theoretical interest, especially if the irradiance levels in the outer ring zones are to be compared to the background irradiance levels. Attention is then given to the energy distribution in point images generated by annular apertures apodized by various transmission functions. The total energy functions are derived; partial energy integrals are determined; and background irradiance functions are discussed.
It is well known that Gaussian apodization of an aperture reduces the sidelobe levels of its point spread function (PSF). In the limit where the standard deviation of the Gaussian function is much smaller than the diameter of the aperture, the sidelobes completely disappear. However, when Gaussian apodization is applied to the Large Deployable Reflector (LDR) array consisting of 84 hexagonal panels, it is found that the sidelobe level only decreases by about 2.5 dB. The reason for this is explained. The PSF is shown for an array consisting of 91 uniformly illuminated hexagonal apertures; this array is identical to the LDR array, except that the central hole in the LDR array is filled with seven additional panels. For comparison, the PSF of the uniformly illuminated LDR array is shown. Notice that it is already evident that the sidelobe structure of the LDR array is different from that of the full array of 91 panels. The PSF's of the same two arrays are shown, but with the illumination apodized with a Gaussian function to have 20 dB tapering at the edges of the arrays. While the sidelobes of the full array have decreased dramatically, those of the LDR array changed in structure, but stayed at almost the same level. This result is not completely surprising, since the Gaussian apodization tends to emphasize the contributions from the central portion of the array; exactly where the hole in the LDR array is located. The two most important conclusions are: the size of the central hole should be minimized, and a simple Gaussian apodization scheme to suppress the sidelobes in the PSF should not be used. A more suitable apodization scheme would be a Gaussian annular ring.
Apodization is often defined in a restricted sense as the suppression of the outer parts (i.e., the concentric rings) of wave optical point images, which results in a higher relative concentration of energy in the central image area. In a wider sense, apodization is defined as any modification of the transmission distribution across the aperture. Generally the modulation transfer function (MTF) is not used in the treatment of apodization. To see how the imaging performance is modified, the MTF is introduced into the discussion. Besides the constant transmission, two transmission distributions which are functions of the aperture radius are considered.
Visual communication, in the form of telephotography and television, for example, can be regarded as efficient only if the amount of information that it conveys about the scene to the observer approaches the maximum possible and the associated cost approaches the minimum possible. Elsewhere we have addressed the problem of assessing the end to end performance of visual communication systems in terms of their efficiency in this sense by integrating the critical limiting factors that constrain image gathering into classical communications theory. We use this approach to assess the electro-optical design of image gathering devices as a function of the f number and apodization of the objective lens and the aperture size and sampling geometry of the phot-detection mechanism. Results show that an image gathering device that is designed to optimize information capacity performs similarly to the human eye. For both, the performance approaches the maximum possible, in terms of the efficiency with which the acquired information can be transmitted as decorrelated data, and the fidelity, sharpness, and clearity with which fine detail can be restored.
The invention relates to a method for reducing a sidelobe impact of low order aberrations using a coronagraph (2) having an apodized occulting mask (10), comprising the steps of: (a) providing in the coronagraph (2) the apodized occulting disk (10) having a transmission profile which graduates from opaque to transparent along its radius and the negative of whose amplitude transmission is a Gaussian profile; (b) determining a predicted sidelobe impact of the aberrations from a particular mix of low order aberration measured in a system as described by the Zernike polynomials; (c) applying the coronagraph to a system point spread function using a given rms width for the Gaussian profile describing the apodized occulting mask (10) and determining an attenuation level of the aberration sidelobes; (d) scaling the Gaussian occulting mask (10) profile to a wider rms width if the sidelobe attenuation level is too low; and (e) repeating the steps (b) through (d) until the attenuation level is acceptable.
A modified coronagraph has been proposed as a prototype of improved notch filters in Raman spectrometers. Coronagraphic notch filters could offer alternatives to both (1) the large and expensive double or triple monochromators in older Raman spectrometers and (2) holographic notch filters, which are less expensive but are subject to environmental degradation as well as to limitations of geometry and spectral range. Measurement of a Raman spectrum is an exercise in measuring and resolving faint spectral lines close to a bright peak: In Raman spectroscopy, a monochromatic beam of light (the pump beam) excites a sample of material that one seeks to analyze. The pump beam generates a small flux of scattered light at wavelengths slightly greater than that of the pump beam. The shift in wavelength of the scattered light from the pump wavelength is known in the art as the Stokes shift. Typically, the flux of scattered light is of the order of 10 7 that of the pump beam and the Stokes shift lies in the wave-number range of 100 to 3,000 cm 1. A notch filter can be used to suppress the pump-beam spectral peak while passing the nearby faint Raman spectral lines. The basic principles of design and operation of a coronagraph offer an opportunity for engineering the spectral transmittance of the optics in a Raman spectrometer. A classical coronagraph may be understood as two imaging systems placed end to end, such that the first system forms an intermediate real image of a nominally infinitely distant object and the second system forms a final real image of the intermediate real image. If the light incident on the first telescope is collimated, then the intermediate image is a point-spread function (PSF). If an appropriately tailored occulting spot (e.g., a Gaussian-apodized spot with maximum absorption on axis) is placed on the intermediate image plane, then the instrument inhibits transmission of light from an on-axis source. However, the PSFs of off-axis light sources are formed off axis - that is, away from the occulting spot - so that they become refocused onto the final image plane.
We present high-contrast images from laboratory testing of a Phase Induced Amplitude Apodization (PIAA) coronagraph at NASA's High Contrast Imaging Testbed (HCIT). Using a deformable mirror and wavefront estimation and control algorithms, we create a 'dark hole' in the monochromatic point-spread function with an inner working angle of (2.05 f lambda/D), with a mean intensity 3.5x10(exp -8). We discuss the contributions to this floor, and the techniques being developed to improve it. We also present simulations that investigate the effect of Lyot stops of various sizes, and conclude that a Lyot stop is necessary for 10(exp -9) performance but that an annular postapodizer is not necessary.
The science instruments (SIs) comprising the James Webb Space Telescope (JWST) Integrated Science Instrument Module (ISIM) were tested in three cryogenic-vacuum test campaigns in the NASA Goddard Space Flight Center (GSFC)'s Space Environment Simulator (SES). In this paper, we describe the results of optical wavefront-error performance characterization of the SIs. The wavefront error is determined using image-based wavefront sensing (also known as phase retrieval), and the primary data used by this process are focus sweeps, a series of images recorded by the instrument under test in its as-used configuration, in which the focal plane is systematically changed from one image to the next. High-precision determination of the wavefront error also requires several sources of secondary data, including 1) spectrum, apodization, and wavefront-error characterization of the optical ground-support equipment (OGSE) illumination module, called the OTE Simulator (OSIM), 2) plate scale measurements made using a Pseudo-Nonredundant Mask (PNRM), and 3) pupil geometry predictions as a function of SI and field point, which are complicated because of a tricontagon-shaped outer perimeter and small holes that appear in the exit pupil due to the way that different light sources are injected into the optical path by the OGSE. One set of wavefront-error tests, for the coronagraphic channel of the Near-Infrared Camera (NIRCam) Longwave instruments, was performed using data from transverse translation diversity sweeps instead of focus sweeps, in which a sub-aperture is translated andor rotated across the exit pupil of the system.Several optical-performance requirements that were verified during this ISIM-level testing are levied on the uncertainties of various wavefront-error-related quantities rather than on the wavefront errors themselves. This paper also describes the methodology, based on Monte Carlo simulations of the wavefront-sensing analysis of focus-sweep data, used to establish the uncertainties of the wavefront error maps.
The science instruments (SIs) comprising the James Webb Space Telescope (JWST) Integrated Science Instrument Module (ISIM) were tested in three cryogenic-vacuum test campaigns in the NASA Goddard Space Flight Center (GSFC)'s Space Environment Simulator (SES) test chamber. In this paper, we describe the results of optical wavefront-error performance characterization of the SIs. The wavefront error is determined using image-based wavefront sensing, and the primary data used by this process are focus sweeps, a series of images recorded by the instrument under test in its as-used configuration, in which the focal plane is systematically changed from one image to the next. High-precision determination of the wavefront error also requires several sources of secondary data, including 1) spectrum, apodization, and wavefront-error characterization of the optical ground-support equipment (OGSE) illumination module, called the OTE Simulator (OSIM), 2) F-number and pupil-distortion measurements made using a pseudo-nonredundant mask (PNRM), and 3) pupil geometry predictions as a function of SI and field point, which are complicated because of a tricontagon-shaped outer perimeter and small holes that appear in the exit pupil due to the way that different light sources are injected into the optical path by the OGSE. One set of wavefront-error tests, for the coronagraphic channel of the Near-Infrared Camera (NIRCam) Longwave instruments, was performed using data from transverse translation diversity sweeps instead of focus sweeps, in which a sub-aperture is translated and/or rotated across the exit pupil of the system. Several optical-performance requirements that were verified during this ISIM-level testing are levied on the uncertainties of various wavefront-error-related quantities rather than on the wavefront errors themselves. This paper also describes the methodology, based on Monte Carlo simulations of the wavefront-sensing analysis of focus-sweep data, used to establish the uncertainties of the wavefront-error maps.
We compare the broadband contrast performances of several Phase Induced Amplitude Apodization (PIAA) coronagraph configurations through modeling and simulations. The basic optical design of the PIAA coronagraph is the same as NASA's High Contrast Imaging Testbed (HCIT) setup at the Jet Propulsion Laboratory (JPL). Using a deformable mirror and a broadband wavefront sensing and control algorithm, we create a "dark hole" in the broadband point-spread function (PSF) with an inner working angle (IWA) of 2(f lambda/D)(sub sky). We evaluate two systems in parallel. One is a perfect system having a design PIAA output amplitude and not having any wavefront error at its exit-pupil. The other is a realistic system having a design PIAA output amplitude and the measured residual wavefront error. We also investigate the effect of Lyot stops of various sizes when a postapodizer is and is not present. Our simulations show that the best 7.5%-broadband contrast value achievable with the current PIAA coronagraph is approximately 1.5x10(exp -8).
The goal of directly imaging Earth-like planets in the habitable zone of other stars has motivated the design of coronagraphs for use with large segmented aperture space telescopes. In order to achieve an optimal trade-o between planet light throughput and di racted starlight suppression, we consider coronagraphs comprised of a stage of phase control implemented with deformable mirrors (or other optical elements), pupil plane apodization masks (gray scale or complex valued), and focal plane masks (either amplitude only or complex-valued, including phase only such as the vector vortex coronagraph). The optimization of these optical elements, with the goal of achieving 10 or more orders of magnitude in the suppression of on-axis (starlight) di racted light, represents a challenging non-convex optimization problem with a nonlinear dependence on control degrees of freedom. We develop a new algorithmic approach to the design optimization problem, which we call the "Auxiliary Field Optimization" (AFO) algorithm. The central idea of the algorithm is to embed the original optimization problem, for either phase or amplitude (apodization) in various planes of the coronagraph, into a problem containing additional degrees of freedom, speci cally ctitious "auxiliary" electric elds which serve as targets to inform the variation of our phase or amplitude parameters leading to good feasible designs. We present the algorithm, discuss details of its numerical implementation, and prove convergence to local minima of the objective function (here taken to be the intensity of the on-axis source in a "dark hole" region in the science focal plane). Finally, we present results showing application of the algorithm to both unobscured o -axis and obscured on-axis segmented telescope aperture designs. The application of the AFO algorithm to the coronagraph design problem has produced solutions which are capable of directly imaging planets in the habitable zone, provided end-to-end telescope system stability requirements can be met. Ongoing work includes advances of the AFO algorithm reported here to design in additional robustness to a resolved star, and other phase or amplitude aberrations to be encountered in a real segmented aperture space telescope.
Recent advances in coronagraph technologies for exoplanet imaging have achieved contrasts close to 1e10 at 4 lambda/D and 1e-9 at 2 lambda/D in monochromatic light. A remaining technological challenge is to achieve high contrast in broadband light; a challenge that is largely limited by chromaticity of the focal plane mask. The size of a star image scales linearly with wavelength. Focal plane masks are typically the same size at all wavelengths, and must be sized for the longest wavelength in the observational band to avoid starlight leakage. However, this oversized mask blocks useful discovery space from the shorter wavelengths. We present here the design, development, and testing of an achromatic focal plane mask based on the concept of optical filtering by a diffractive optical element (DOE). The mask consists of an array of DOE cells, the combination of which functions as a wavelength filter with any desired amplitude and phase transmission. The effective size of the mask scales nearly linearly with wavelength, and allows significant improvement in the inner working angle of the coronagraph at shorter wavelengths. The design is applicable to almost any coronagraph configuration, and enables operation in a wider band of wavelengths than would otherwise be possible. We include initial results from a laboratory demonstration of the mask with the Phase Induced Amplitude Apodization coronagraph.