Beam propagation simulations for LISA in the presence of telescope aberrations

Kenny, Fiona; Devaney, Nicholas

doi:10.1088/1361-6382/abccdd

Cited by 7 publications

(6 citation statements)

References 16 publications

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“…Recently, Ming et al made an analytical analysis to confirm that large defocus and small coma is helpful to make the stationary point close to the central axis and reduce the phase noise [9]. Based on Bessel function expressions, Vinet et al built a far-field optical model and proposed an extreme requirement of the wavefront aberration of the telescope [10]. Kenny et al analyzed the first 11 Zernike aberrations and revealed only even index terms will contribute to the far-field phase [11].…”

Section: Introductionmentioning

confidence: 99%

The analysis of the far-field phase and the tilt-to-length error contribution in space-based laser interferometry

Xiao

Duan

Min

et al. 2023

Class. Quantum Grav.

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The arm length of the space-based interferometer for gravitational wave detection is 108~109 m, and picometer precision is required. The wavefront error in the far-field coupled with the pointing jitter is a major noise source, which raises higher requirements of the wavefront quality of the telescope. By extending the analytical solutions of the far-field phase to 21 Zernike aberrations, this paper demonstrates that the far-field phase could be regarded as the sum of the effects of the individual aberrations and a phase plane with its slope related to the wavefront RMS. For individual aberrations, only low-order aberrations have a significant effect on the far-field phase, but high-order aberrations will contribute to the coupling terms which is shown as a phase slope. So there is a definite corresponding relationship between the aberrations and the far-field phase, and it can be easily illustrated graphically. Based on the analytical solutions of the far-field phase, we proposed to consider the tilt-to-length (TTL) error together with the far-field phase. The TTL error is also one of the main noise sources in space-based laser interferometry, which presents big difficulties in the optical system. We found that TTL error could be added to the far-field phase as a piston term during pointing, which then help to bring the stationary point closer to the z-axis and reduce the phase noise detected at the stationary point. By considering the TTL together with the far-field phase, the requirement of the telescope could be /25 wavefront RMS (=1064 nm). And there will be a large tolerance range for the TTL error, so it is only necessary to evaluate the TTL error and limit it to a suitable range, not to eliminate it.

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Section: Introductionmentioning

confidence: 99%

The analysis of the far-field phase and the tilt-to-length error contribution in space-based laser interferometry

Xiao

Duan

Min

et al. 2023

Class. Quantum Grav.

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“…[11] The numerical simulation is used to describe the effect of an aberrated transmitting telescope on the light collected by the receiving telescope with Zernike modes. [12] Via calculations of the wavefront aberrations in the far field, an end-to-end investigation of the measurement noise due to the interaction between the telescope jitters and wavefront aberrations is reported in Ref. [13].…”

Section: Introductionmentioning

confidence: 99%

Estimation of far-field wavefront error of tilt-to-length distortion coupling in space-based gravitational wave detection

Tao¹,

Jin²,

Wu³

2023

Chinese Phys. B

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In space-based gravitational wave detection, the estimation of far-field wavefront error of the distorted beam is the precondition for the noise reduction. Zernike polynomials is used to describe the wavefront error of the transmitted distorted beam. The propagation of a laser beam between two telescope apertures is calculated numerically. Far-field wavefront error is estimated with the absolute height of the peak-to-valley phase deviation between distorted Gaussian beam and a reference distortion-free Gaussian beam. The results show the pointing jitter is strongly related to the wavefront error. Furthermore, when jitter decreases 10 times from 100 to 10 nrad, wavefront error reduces for more than an order of magnitude. In the analysis of multi-parameter minimization, the minimum of wavefront error tends to Z[5,3] Zernike in some parameter ranges. Some Zernikes have a strong correlation with wavefront error of the received beam. When the aperture diameter increases at Z[5,3] Zernike, wavefront error is not monotonic and has oscillation. Nevertheless, wavefront error almost remains constant with the arm length increasing from 10-1 Mkm to 103 Mkm. When the arm length decreases for three orders of magnitude from 10-1 Mkm to 10-4 Mkm, wavefront error has only an order of magnitude increasing. In the range of 10-4 Mkm to 103 Mkm, the lowest limit of the wavefront error is from 0.5 fm to 0.015 fm, at Z[5,3] Zernike and 10 nrad jitter.

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“…Our analysis of TTL noise induced by WFE begins in section 2 as a first order expansion in SC jitter components coupling to the received field's phase gradient, yielding two TTL coupling components to two jitter degrees of freedom. This first order expansion in jitter allows for actual recovery of expected TTL noise as a function of receiving SC location, in contrast to methodologies of prior studies [18,19] where the TTL is defined more as a statistic over the entire map. We discuss how gradients are obtained via a Hermite-Gaussian (HG) modal decomposition based propagation of an approximation in our initial beam, and the limitations of this approximation.…”

Section: Introductionmentioning

confidence: 99%

“…Having verified the accuracy of these expansions, the maps associated with polynomial terms show only some Zernikes within WFE, specified in section 4, couple significantly to TTL noise. We can then neglect a significant number of unimportant terms in the expansions, further speeding up this fast modeling technique without a loss of accuracy, allowing for more extensive simulations than those of prior studies [18,19].…”

Section: Introductionmentioning

confidence: 99%

Wavefront error based tilt-to-length noise analysis for the LISA transmitted beam

Weaver

Mueller

Fulda

2022

Class. Quantum Grav.

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The Laser Interferometer Space Antenna (LISA) will open the signal-rich 100 μHz to 1 Hz gravitational wave window. LISA is expected to be limited by acceleration noise in the low frequency range and noise associated with the optical measurement system above a few mHz. Of the latter, apparent length changes due to spacecraft angular jitter are among the most critical contributors. One of the coupling mechanisms is via wavefront error in the transmitted beam. Utilizing a Zernike polynomial decomposition of such wavefront error, we introduce and explore the validity of extremely fast best fit polynomial expansion based noise recreation tools that provide a clear picture for which transmit beam perturbations couple most strongly with spacecraft jitter into LISA noise.

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Beam propagation simulations for LISA in the presence of telescope aberrations

Cited by 7 publications

References 16 publications

The analysis of the far-field phase and the tilt-to-length error contribution in space-based laser interferometry

The analysis of the far-field phase and the tilt-to-length error contribution in space-based laser interferometry

Estimation of far-field wavefront error of tilt-to-length distortion coupling in space-based gravitational wave detection

Wavefront error based tilt-to-length noise analysis for the LISA transmitted beam

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