Fresnel phasing of segmented mirror telescopes

Shack-Hartmann (S-H) phasing of segmented telescopes is based upon a physical optics generalization of the geometrical optics Shack-Hartmann test, in which each S-H lenslet straddles an intersegment edge. For the extremely large segmented telescopes currently in the design stages, one is led naturally to very large pupil demagnifications for the S-H phasing cameras. This in turn implies rather small Fresnel numbers F for the lenslets; the nominal design for the Thirty Meter Telescope calls for F=0.6. For such small Fresnel numbers, it may be possible to eliminate the lenslets entirely, replacing them with a simple mask containing a sparse array of clear subapertures and thereby also eliminating a number of manufacturing problems and experimental complications associated with lenslets. We present laboratory results that demonstrate the validity of this approach.     

On-sky multiwavelength phasing of segmented telescopes with the Zernike phase contrast sensor

Future extremely large telescopes will adopt segmented primary mirrors with several hundreds of segments. Cophasing of the segments together is essential to reach high wavefront quality. The phasing sensor must be able to maintain very high phasing accuracy during the observations, while being able to phase segments dephased by several micrometers. The Zernike phase contrast sensor has been demonstrated on-sky at the Very Large Telescope. We present the multiwavelength scheme that has been implemented to extend the capture range from ±λ/2 on the wavefront to many micrometers, demonstrating that it is successful at phasing mirrors with piston errors up to ±4.0 μm on the wavefront. We discuss the results at different levels and conclude with a phasing strategy for a future extremely large telescope.     

On-sky performances of an optical phasing sensor based on a cylindrical lenslet array for segmented telescopes

New optical phasing sensor technologies have been studied with a test bench experiment, called Active Phasing Experiment, on-sky at the European Southern Observatory Very Large Telescope. One of the sensors was of the Shack-Hartmann type using cylindrical lenslets across the segment borders for the measurement of the phasing errors. With bright stars, the precision of the measurement of piston steps at a single border was better than 9 nm wavefront RMS, and the precision of the closed-loop correction of the piston errors of the segments across the whole mirror was better than 10 nm wavefront RMS. With dimmer stars of magnitude up to 14.5, precisions of the order of 22 nm wavefront RMS were obtained.     

Holographic correction and phasing of large sparse-array telescopes

I have constructed a 1-m-diameter telescope using separate, low-quality spherical primary mirror segments. A single hologram of the mirrors is used to correct the random surface distortions as well as spherical aberration, while simultaneously phasing the individual apertures together. I present experimental results of the removal of an error of thousands of waves to produce a diffraction-limited instrument operating over a narrow bandwidth. This technique promises to have many benefits in future space-based telescopes for imaging, lidar, and optical communications.     

Fabrication and alignment issues for segmented mirror telescopes

There is a great demand for new telescopes that use larger primary mirrors to collect more light. Because of the difficulty in the fabrication of mirrors larger than 8 m as a single piece, they must be made with numerous smaller segments. The segments must fit together to create the effect of a single mirror, which presents unique challenges for fabrication and testing that are absent for monolithic optics. This is especially true for the case of a highly aspheric mirror required to make a short two-mirror telescope. We develop the relationship between optical performance of the telescope and errors in the manufacture and operation of the individual segments.     

Testing and applicability of the UPC-ZEBRA interferometer as a phasing system in segmented-mirror telescopes

In segmented-mirror telescopes, wave-front discontinuities caused by segment misalignment are a major problem because they severely degrade optical performance. While angular misalignments are usually measured with deflectometric wave-front sensors (e.g., Shack-Hartmann sensors), a number of techniques have been proposed for the measurement of vertical discontinuities (pistons). In earlier papers we presented an instrument called UPC-ZEBRA that uses a novel interferometric technique to measure piston error during the daytime with an uncertainty of 5 nm within a 30-microm range. Here we present the most representative results obtained during the testing stage and a detailed analysis of error sources. The main modifications to be introduced for the instrument's use as a phasing calibration system are also outlined.     

Analytical study of diffraction effects in extremely large segmented telescopes

We present an analysis of the diffraction effects from a segmented aperture with a very large number of segments-prototype of the next generation of extremely large telescopes. This analysis is based on the point-spread-function analytical calculation for Keck-type hexagonal segmentation geometry. We concentrate on the effects that lead to the appearance of speckles and/or a regular pattern of diffraction peaks. These effects are related to random piston and tip-tilt errors on each segment, gaps between segments, and segment edge distortion. We deliver formulas and the typical numerical values for the Strehl ratio, the relative intensity of higher-order diffraction peaks, and the averaged intensity of speckles associated with each particular case of segmentation error.     

Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm

To achieve its full diffraction limit in the infrared, the primary mirror of the Keck telescope (now telescopes) must be properly phased: The steps or piston errors between the individual mirror segments must be reduced to less than 100 nm. We accomplish this with a wave optics variation of the Shack-Hartmann test, in which the signal is not the centroid but rather the degree of coherence of the individual subimages. Using filters with a variety of coherence lengths, we can capture segments with initial piston errors as large as +/-30 microm and reduce these to 30 nm--a dynamic range of 3 orders of magnitude. Segment aberrations contribute substantially to the residual errors of approximately 75 nm.     

Phasing the mirror segments of the Keck telescopes II: the narrow-band phasing algorithm

In a previous paper, we described a successful technique, the broadband algorithm, for phasing the primary mirror segments of the Keck telescopes to an accuracy of 30 nm. Here we describe a complementary narrow-band algorithm. Although it has a limited dynamic range, it is much faster than the broadband algorithm and can achieve an unprecedented phasing accuracy of approximately 6 nm. Cross checks between these two independent techniques validate both methods to a high degree of confidence. Both algorithms converge to the edge-minimizing configuration of the segmented primary mirror, which is not the same as the overall wave-front-error-minimizing configuration, but we demonstrate that this distinction disappears as the segment aberrations are reduced to zero.     

Phase discontinuity sensing: a method for phasing segmented mirrors in the infrared

We describe a novel method for phasing segmented optics in which the signal is the difference between inside-of-focus and outside-of-focus long-exposure infrared images. A detailed algorithm based on a correlation of this difference image with theoretical images or templates is presented. In a series of tests of this phase discontinuity sensing (PDS) algorithm at the Keck 1 telescope, at a wavelength of 3.3 mum, the rms piston error (averaged over the 36 primary mirror segments) was repeatedly reduced from approximately 240 to 40 nm or less. Furthermore, the PDS phasing solution was consistent with our previous phasing camera results (to within 66-nm rms), providing strong independent confirmation of this earlier approach.     

Design of an interferometric system for the measurement of phasing errors in segmented mirrors

One of the new problems that has to be solved for segmented mirrors is related to periodic phasing, because for such mirrors to exhibit diffraction-limited performance the segments have to be positioned with an accuracy of a fraction of a wavelength. We describe the optical design of an instrument that measures the phasing errors (i.e., tip, tilt, and piston) between two segments under daylight conditions. Its design is based on a high-aperture white-light Michelson interferometer. It was developed at the Center for Sensors, Instruments and Systems Development (CD6) of the Technical University of Catalunya, Spain, and its final testing was carried out on the Gran Telescopio Canarias test workbench.     

Mach-Zehnder interferometer for piston and tip-tilt sensing in segmented telescopes: theory and analytical treatment

A study is presented of a Mach-Zehnder interferometer for the measurement of phasing errors of the type found in segmented telescopes. We show that with a pinhole much larger than the Airy disk and an optical path difference between the arms equal to a quarter of the wavelength, the interferometric signal is related to the second derivative of the wave front. In this condition the signal is produced mostly by the segmentation errors and is marginally sensitive to other aberrations including atmospheric turbulence. The signal has distinguishable symmetric and antisymmetric properties that are related to segment aberrations. We suggest using the antisymmetric component of the signal to retrieve piston, tip, and tilt. The symmetric component of the signal serves as an estimate of the measurement error. In this way we proceed with a study of the errors associated with the misalignment of the interferometer, the segment edge imperfections, and the nonaveraged atmospheric perturbations. The entire study is performed on a theoretical basis, and numerical simulations are used to cross check the analytical results.     

Arbitrary phasing technique for two-dimensional coherent laser array based on an active segmented mirror

We introduce a novel (to the best of our knowledge) phasing technique for a coherent laser array. We have accomplished arbitrary phasing in the interval 0-π. A seven-channel laser array experiment is built for verification. A custom-made beam arraying structure is designed to arrange beamlets into a two-dimensional hexagonal array. In the phase-locking loop, the wavefront sensing is performed interferometrically. An active segmented mirror is used for phasing, and the control signals are generated by the proportional control algorithm. In experiment, all the beamlets have been properly phased, and the experiment of inertia-free beam steering has been accomplished.     

Strehl ratio and modulation transfer function for segmented mirror telescopes as functions of segment phase error

We derive the Strehl ratio for a segmented mirror telescope as a function of the rms segment phase error and the observing wavelength, with and without the effects of the atmosphere. A simple analytical expression is given for the atmosphere-free case. Although our specific results are in the context of the Keck telescope, they are presented in a way that should be readily adaptable to other segmented geometries. We also derive the corresponding modulation transfer functions. These results are useful in determining how accurately a segmented mirror telescope needs to be phased for a variety of observing applications.     

Tip-tilt error for extremely large segmented telescopes: detailed theoretical point-spread-function analysis and numerical simulation results

We present an analysis of point-spread functions for segmented mirrors affected by random tip-tilt errors on each segment. In addition to Strehl ratio evaluation, this analysis considers key characteristics such as the intensity and the location of speckles and secondary peaks and the relative energy distribution between these features. We develop a method to describe the shape of a nonaveraged point-spread function and deduce the final expressions for ensemble-averaged characteristics. Based on Keck-type hexagonal segmentation geometry, our study is extended to an arbitrary number of segments, and we describe qualitatively the transition from the case of a mirror with few segments to that of a mirror with several hundred segments--prototype of the next generation of Extremely Large Telescopes.     

Phasing segmented mirrors: a modification of the Keck narrow-band technique and its application to extremely large telescopes

Future telescopes with diameters greater than 10 m, usually referred to as extremely large telescopes (ELTs), will employ segmented mirrors made up of hundreds or even thousands of segments, with tight constraints on the piston errors between individual segments. The 10-m Keck telescopes are routinely phased with the narrow-band phasing technique. This is a variation of the Shack-Hartmann wave-front sensor in which the signal is the correlation between individual subimages and simulated images. We have investigated the applicability of this technique to ELTs, and in the process we have developed what to our knowledge is a new algorithm in which each subimage provides on its own a piston-dependent value. We also discuss an alternative algorithm to resolve the lambda ambiguity that allows detection of problematic cases, and a modification of the singular-value-decomposition procedure used to phase the whole mirror, using weightings on individual measurement errors. By means of simulations we show that the modified technique shows improved performance and that it can work with sufficient precision on telescopes as large as 100 m.     

Terahertz astronomical telescopes and instrumentation

The terahertz (THz) region of the electromagnetic spectrum is of great importance for astrophysics. In fact, it is central to the whole field of experimental cosmology. This paper outlines the range of astrophysical problems that can be answered by observing at THz frequencies, describes some of the major THz astronomical telescopes that are being constructed, and gives a vision of the way in which the technological development of superconducting very-large-scale integration circuit technology and solid-state source technology will lead to major advances in the subject.     

Accommodation of speckle in object-based phasing

This work addresses the physical basis of the measurement process for object-based phasing of an array of telescopes. In this regard an enhanced least-squares estimator that is capable of differentiating among three families of array aberrations in an object-based phasing system is developed. In a system of this nature the system to be phased illuminates the object of interest and the return radiation is detected. Telescope aberrations, atmospheric aberrations, and speckle-induced aberrations are all reported by the estimator to facilitate correction of telescope and atmospheric aberrations. This is accomplished by proper handling of the unobservable modes and recognizing that the five global aberrations-telescope array piston, atmospheric array piston and tilt, and speckle array piston and tilt-cannot be measured accurately so they need to be projected out of the estimated piston commands. Except for these relatively benign array aberrations, the disturbances for all three families of array aberrations are estimated exactly. An interesting feature of the speckle array aberrations is that a synthetic aperture is developed that is almost twice as large as the array of telescopes under consideration.     

Maksutov’s cameras and telescopes

The third-order aberration formulae we have proposed in a previous paper, starting from Fermat’s principle and from the idea of stigmatic paths, are here applied to analyze and to project Maksutov’s cameras and Maksutov-Cassegrain’s telescopes. The final projects, since they take into account the thickness of lenses and the fifth-order aberrations, do not need any optimization procedure.     

Sensitivity of coded mask telescopes

Simple formulas are often used to estimate the sensitivity of coded mask x-ray or gamma-ray telescopes, but these are strictly applicable only if a number of basic assumptions are met. Complications arise, for example, if a grid structure is used to support the mask elements, if the detector spatial resolution is not good enough to completely resolve all the detail in the shadow of the mask, or if any of a number of other simplifying conditions are not fulfilled. We derive more general expressions for the Poisson-noise-limited sensitivity of astronomical telescopes using the coded mask technique, noting explicitly in what circumstances they are applicable. The emphasis is on using nomenclature and techniques that result in simple and revealing results. Where no convenient expression is available a procedure is given that allows the calculation of the sensitivity. We consider certain aspects of the optimization of the design of a coded mask telescope and show that when the detector spatial resolution and the mask to detector separation are fixed, the best source location accuracy is obtained when the mask elements are equal in size to the detector pixels.