Aberrated Optics Validation
The LSST active optics system (AOS) is designed to minimize optical aberrations by modifying the positions and surface figures of telescope components in real time. The LSST AOS is comprised of two separate systems. The open loop control system uses a lookup table to compensate for errors that are constant in time. These errors are mostly comprised of errors in the fabrication and construction of LSST. The closed loop control system uses wavefront sensors to detect slowly varying optical aberrations. This includes thermally and gravitationally induced shifts and low spatial order surface errors for each optical element.
In the ideal case the AOS would be able to remove all optical aberrations introduced by the LSST optics system. However, in practice there are small, residual deviations that contribute to the PSF. Our goal is to simulate these residual errors and determine the induced optical aberrations. At present, we restrict ourselves to considering errors left uncorrected by the closed-loop control system. This does not include errors introduced by noise in the closed loop corrections.
Daniel Perrefort, Aaron Roodman, Josh Meyers, Bo Xin
- The aberrated optics modeled by ImSim is based on the LSST adaptive optics system
(AOS) as outlined in Angeli, Xin et. al 2014 - A general overview on wavefront aberrations can be found in Aron Roodman's DE School talk from 2016.
- Zemax estimates for the nominal state of the LSST optics system were provided by Aaron Roodman
- Values for the sensitivity matrix outlined in Angeli, Xin et. al 2014 were provided by Bo Xin.
Optical aberrations can be described by a superposition of Zernike Polynomials
. These polynomials form a
complete set of functions, each of which represents a unique optical aberration. For
coordinates
in the focal plane
of LSST and
in the exit pupil,
we write this superposition as
Note that the coefficients are
position dependent. Given an arbitrary coordinate, these coefficients provide a description of
the strength and phase of each aberration introduced by the optics system. We can express
these coefficients in terms of their nominal value
and deviations from that
nominal value
.
The nominal Zernike coefficients are estimated using the Zemax model. These will differ slightly from the real LSST, however an “as-built” Zemax model will not be available until closer to the completion of construction.
Since we are only considering slowly changing optical errors, in the present context
represents the residual aberrations from the closed loop system.
The AOS consists of 50 degrees of freedom which are varied by the closed loop system.
Deviations in each degree of freedom are represented by a set of 50 normal distributions.
From these distributions, the aberrated optics model generates a random set of optical
deviations representing an independent state of the LSST optics system. These deviations are
then mapped to the corresponding Zernike coefficients using the sensitivity matrix
outlined in Angeli, Xin et. al
2014
The sensitivity matrix, and by extension
,
has been simulated for 35 positions in the LSST focal plane. In order to determine
at an arbitrary location, we
perform a 2-D fit for each Zernike coefficient in position space. Since the Zernike polynomials
are a complete set of functions in a circular aperture, we use a superposition
of Zernike polynomials to perform this fit. Note that this superposition is not the same as the
first Equation above.
- For zero deviations from the nominal state, the aberrated optics model should return values in agreement with current Zemax estimates. This condition is enforced in the ImSim test suite.
- Random samples of optical deviations should form a normal distribution centered on zero. This represents our expectation that the optical system will (on average) oscillate around the nominal state.
- The average PSF due strictly to the optical system should be physically reasonable over a large collection of random optical states.
Condition (2) is demonstrated for a subset of optical degrees of freedom in Figure 1. Figure 2 demonstrates the Zernike Coefficients corresponding to the LSST optical system's nominal state. Figures 3 and 4 demonstrate the Zernike coefficients derived for a random set of deviations in each degree of freedom, both sampled discreetly and fitted using a superposition of Zernike Polynomials.
Figure 1: A set of 1000 perturbations in the LSST optical system that cause deviations from the nominal state (zero). Demonstrated for the first twelve optical degrees of freedom, these deviations are derived from a set of unique Gaussian distributions centered at zero. Units vary depending on the degree of freedom.
Figure 2: A set of nominal Zernike Coefficients sampled for 35 locations in the exit pupil of LSST. These coefficients collectively represent the nominal state of the LSST optical system. Coefficients are shown in units of observed wavelength.
Figure 3: A set of randomly generated Zernike Coefficients for 35 locations in the exit pupil of LSST. These coefficients include random deviations from the nominal state and represent a distinct state of the LSST optical system. Coefficients are shown in units of observed wavelength.
Figure 4: A two dimensional fit of randomly generated Zernike Coefficients in the exit pupil of LSST. Coefficients are shown in units of observed wavelength.
Progress on improvments to this model are currently being tracked in issue LSSTDESC/imSim#128. Please see this issue for the most up to date information.
In LSSTDESC/DC2-production#259 it was pointed out that the modeled PSF's are too round. Some of this was attributed to identified bugs, but it did not fully solve the problem. The issue mentions that the undersampling of the focal plane might effect the ellipticity of the optical PSF by introducing vertical and horizontal symmetry. In particular, the sampling points happen to be at the nodes of Z19, and the peaks/valleys of Z18 (see https://www.telescope-optics.net/images/zernike_noll.PNG)
It was also pointed out that the modeled deviations might be too close to the nominal optical model, and we need to allow more variation in the simulated deviations. The current optical model only considers a small part of the deviations that the optical system will introduce. Since we are specifically modeling effects that are uncorrected by the closed-loop system - which handles slowly varying errors - our models are only an approximation.
As a temporary stop-gap PR LSSTDESC/imSim#164 reduces the FoV fitting function from Z4 through Z22 to Z4 through Z15. It also multiplies amplitudes of the optics misalignments by an artificial factor of 3.