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Register a new userMoment analysis of focus-diverse point spread functions for modal wavefront sensing of uniformly illuminated circular-pupil systems
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Hanshin Lee
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A new concept of using focus-diverse point spread functions (PSFs) for modal wavefront sensing (WFS) is explored. This is based on relatively straightforward image moment analysis of measured PSFs, which differentiates it from other focal-plane wavefront sensing techniques (FPWFS). The presented geometric analysis shows that the image moments are non-linear functions of wave aberration coefficients, but notes that focus-diversity (FD) essentially decouples the coefficients of interest from others, resulting in a set of linear equations whose solution corresponds to modal coefficient estimates. The presented proof-of-concept simulations suggest the potential of the concept in WFS with strongly aberrated high SNR objects in particular.
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The shape of a focus-modulated point spread function (PSF) is used as a quick visual assessment tool of aberration modes in the PSF. Further analysis in terms of shape moments can permit quantifying the modal coefficients with an accuracy comparable to that of typical wavefront sensors. In this letter, the error of the moment-based wavefront sensing is analytically described in terms of the pixelation and photon/readout noise. All components highly depend on the (unknown) PSF shape, but can be estimated from the measured PSF sampled at a reasonable spatial resolution and photon count. Numerical simulations verified that the models consistently predicted the behavior of the modal estimation error of the moment-based wavefront sensing.
One of the problems often encountered in X-ray mirror manufacturing is setting proper manufacturing tolerances to guarantee an angular resolution - often expressed in terms of Point Spread Function (PSF) - as needed by the specific science goal. To do this, we need an accurate metrological apparatus, covering a very broad range of spatial frequencies, and an affordable method to compute the PSF from the metrology dataset. [...] However, the separation between these spectral ranges is difficult do define exactly, and it is also unclear how to affordably combine the PSFs, computed with different methods in different spectral ranges, into a PSF expectation at a given X-ray energy. For this reason, we have proposed a method entirely based on the Huygens-Fresnel principle to compute the diffracted field of real Wolter-I optics, including measured defects over a wide range of spatial frequencies. Owing to the shallow angles at play, the computation can be simplified limiting the computation to the longitudinal profiles, neglecting completely the effect of roundness errors. Other authors had already proposed similar approaches in the past, but only in far-field approximation, therefore they could not be applied to the case of Wolter-I optics, in which two reflections occur in sequence within a short range. The method we suggest is versatile, as it can be applied to multiple reflection systems, at any X-ray energy, and regardless of the nominal shape of the mirrors in the optical system. The method has been implemented in the WISE code, successfully used to explain the measured PSFs of multilayer-coated optics for astronomic use, and of a K-B optical system in use at the FERMI free electron laser.
The basic outline of a pupil plane WaveFront Sensor is reviewed taking into account that the source to be sensed could be different from an unresolved source, i.e. it is extended, and that it could deploy also in a 3D fashion, enough to exceed the fields depth of the observing telescope. Under these conditions it is pointed out that the features of the reference are not invariant for different position on the pupil and it is shown that the INGOT WFS is the equivalent of the Pyramid for a Laser Guide Star. Under these conditions one can imagine to use a Dark WFS approach to improve the SNR of such a WFS, or to use a corrected upward beam in order to achieve a better use of the LGS photons with respect to an ideal Shack-Hartmann WFS.
We present a new concept of an integrated optics component capable of measuring the complex amplitudes of the modes at the tip of a multimode waveguide. The device uses a photonic lantern to split the optical power carried by an $N$-modes waveguide among a collection of single-mode waveguides that excite a periodic array of at least $N^2$ single-mode evanescently-coupled waveguides. The power detected at each output of the array is a linear combination of the products of the modal amplitudes-a relation that can, under suitable conditions, be inverted allowing the derivation of the amplitudes and relative phases of the modal mixture at the input. The expected performance of the device is discussed and its application to the real-time measurement of modal instability in high power fiber lasers is proposed.
An optical imaging system forms an object image by recollecting light scattered by the object. However, intact optical information of the object delivered through the imaging system is deteriorated by imperfect optical elements and unwanted defects. Image deconvolution, also known as inverse filtering, has been widely exploited as a recovery technique because of its practical feasibility, and operates by assuming the linear shift-invariant property of the imaging system. However, shift invariance is not rigorously hold in all imaging situations and it is not a necessary condition for solving the inverse problem of light propagation. Here, we present a method to solve the linear inverse problem of coherent light propagation without assuming shift invariance. Full characterization of imaging capability of the system is achieved by successively recording optical responses, using various laser illumination angles which are systematically controlled by a digital micro-mirror device. Experimental results show that image distortions caused by optical defocus can be restored by conventional deconvolution, but severe aberrations produced by a tilted lens or an inserted disordered layer can be corrected only by the proposed generalized image deconvolution. This work generalizes the theory of optical imaging and deconvolution, and enables distortion-free imaging under any general imaging condition.
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