TipTop - Error Terms Coverage

TipTop is an analytical PSF reconstruction tool.
It covers the main AO error terms through PSD-based modeling on the HO side, and a jitter kernel on the LO side. Telescope/instrument effects can be partially included (via static OTFs), while other calibration/engineering residuals are out of scope.

High-Order (HO) Errors ✅

The HO part of TipTop is built from Power Spectral Densities (PSDs).
Each term is computed independently, then summed in the AO control space and Fourier-transformed into the HO PSF.

Included PSDs

• Fitting error
  – Residuals above the DM cutoff frequency (∝ actuator pitch).
  – Includes what other budgets call “generalized” and “HF fitting” terms.

• Noise error
  – Photon noise, read-out noise, and background propagated through the reconstructor (tomographic if relevant).
  – Propagated in time through the AO controller transfer functions.

• Aliasing error
  – High spatial frequencies folded back by WFS sampling.
  – Approximated from SCAO geometry, applied to other AO modes.

• Temporal error
  – Servo-lag, bandwidth, delay effects.
  – Computed via rejection transfer functions of the chosen controller (integrator, double integrator, etc.).

• Tomographic error
  – From imperfect reconstruction of turbulence volume, including LGS cone effect.
  – Covers SCAO anisoplanatism, tomography with multiple LGS/NGS, and projection onto DMs.

• Chromatism & Differential Refraction
  – Added explicitly as PSD terms in the HO error budget.

• MCAO/LGS volume loss
  – Dedicated term for reduced WFS information when using LGS in MCAO.

Summary of the different PSDs used in the HO part of TIPTOP. The first one is the fitting term, followed by temporal, noise, aliasing, etc. All PSDs are then summed and converted into the HO PSF. (source: Neichel et al., "TipTop: toward a single tool for all ELT instrument’s PSF prediction", Adaptive Optics Systems IX, 2024)

Low-Order (LO) / Jitter ✅

The LO kernel accounts for residual image motion. It is modeled as the quadratic sum of three independent terms (Plantet et al. 2018):

• Residual windshake / vibrations
  – Telescope vibration PSD filtered by control law (integrator/double integrator).
  – Optimized on brightest NGS SNR.
  – Assumed isoplanatic.

• LO tomography
  – Difference between turbulence volume seen by NGS and science directions.
  – Reduces to TT anisoplanatism for single NGS.

• Tip-tilt noise
  – Propagation of TT sensor noise through the control loop.
  – Depends on SR/FWHM at NGS position, lenslet pitch, RON, magnitude, and λ.
  – With multiple NGS: propagated through the LO reconstructor.

Telescope / Instrument Effects ⚠️

• Static OTF (optional):
  User can supply static aberrations from telescope or instrument (pupil maps, NCPA, off-axis aberrations).

• Detector sampling:
  Pixellation included in final PSF generation.

• Not included:
  – Dome seeing residuals
  – Low-wind effect
  – Rayleigh scattering
  – Vibrations of post-focal DMs
  – Sodium layer variability
  – WFS spot truncation
  – Calibration/RTC update residuals
  

Summary Table

Domain	Error term	Status
HO	Tomography, fitting, noise, aliasing, temporal, chromatic, refraction, cone effects	✅ Included
LO	Windshake/vibrations, LO tomography, Tip-Tilt noise, anisoplanatism	✅ Included
Telescope/Instr.	Static OTF aberrations, pixel sampling	⚠️ Partial (user-supplied or approximated)
	Dome seeing, low-wind effect, DM vibrations, sodium profile variations, Rayleigh, calibration terms	❌ Not included

Detailed Error Source Mapping

Click to expand detailed error coverage

Category	Error Source	In TipTop?	Notes
High Orders	Tomographic error	✅ Included	Included in HO spatio-temporal PSD (MMSE / POLC, cone effect).
	Generalized fitting error	✅ Included	Covered by DM fitting PSD (actuator pitch).
	HF fitting error	⚠️ Partial	Absorbed in fitting term, not a separate PSD.
	Measurement noise error	✅ Included	WFS noise propagated through reconstructor + temporal loop
	Temporal error	✅ Included	Servo-lag / bandwidth explicitly modeled.
Reference Loop	Correction residual	✅ Included	Combination of fitting + temporal + noise + aliasing.
	Truncation error	❌ Not included	WFS spot truncation (elongated sodium) not modeled.
	Sodium Profile Variations	❌ Not included	Not included; assumes fixed sodium profile.
	Propagation of atmospheric disturbances	✅ Included	Encoded in tomography PSD.
	Non common field aberrations	⚠️ Partial	Can be added via static OTF if user provides maps.
MORFEO relay	Design, Manufacturing, Alignment of PFRO	❌ Not included	Instrument residuals not modeled.
	Optical effects of air in the PFRO	❌ Not included	Not included.
	Fitting error on DM1	✅ Included	Included via DM fitting PSD (configurable).
	Fitting error on DM2	✅ Included	Same as above.
	Vibrations of post focal DMs	❌ Not included	Not modeled (only telescope windshake).
Calibration errors	Actuators / sub-apertures mismatch	❌ Not included	Not explicitly included.
	Periodic update of RTC control matrices	❌ Not included	Not modeled.
Telescope	Residual HO Telescope (M1 & M2)	⚠️ Partial	Can be included as static OTF (if provided).
	Telescope dome seeing residual	❌ Not included	Not included.
	Low-Wind Effect	❌ Not included	Not modeled.
	Telescope Off-Axis aberrations	⚠️ Partial	Possible via static OTF if maps supplied.
Low Orders	Residual Windshake	✅ Included	Modeled in LO kernel via vibration PSD + controller.
	Tomographic error	✅ Included	LO tomography, reduces to Tip-Tilt anisoplanatism if single NGS.
	Temporal + Measurement noise error	✅ Included	Tip-Tilt noise propagated through loop.
Field average focus	Temporal + Measurement noise error	⚠️ Partial	Focus variations across field not explicitly separated; Not isolated; some contribution in LO error budgets.
	Anisoplanatism error	✅ Included	Covered by LO tomography.
	Telescope	⚠️ Partial	Jitter kernel includes telescope vibration; no dome seeing.
Other errors	Atmospheric Chromatism	✅ Included	Explicit PSD term in HO.
	Rayleigh scattering	❌ Not included	Not modeled.
	Non-modelled errors	❌ Not included	By definition.
	Contingency	❌ Not included	By definition.

✅ Included → TIPTOP computes it.
⚠️ Partial → only if user provides static inputs, or absorbed in another term.