Shack-Hartmann Sensor
SHWFS design: spot size, centroid precision, sensitivity, dynamic range, and sub-aperture layout.
Lenslets in pupil
500
26.7 across; 108 more partly lit
Spot diameter (zero to zero)
84.4 µm
FWHM 37.4 µm = 6.8 px
Dynamic range θ_max
5.39 mrad
68.2 waves PV tilt over the pupil
Strehl ratio (Maréchal)
0.782
0.079 waves RMS
Max defocus
1.35 D
17.0 waves PV
Wavefront per pixel shift
82.5 nm/px
Tilt 275 µrad/px
Centroid noise (1000 photons)
0.502 µm
7.53 nm wavefront per lenslet
Fresnel number d²/λf
7.11
Spot fits a lenslet above 2
Formulas (textbook approximation)
Δx = f·∂W/∂x — local wavefront tilt moves the spot
Spot: first zero ρ₀ = λf/d (square) or 1.22λf/d (circular); FWHM 0.886 or 1.029 λf/d
θ_max = (d − 2ρ₀)/(2f); PV tilt θ_max·D, PV defocus θ_max·D/4, defocus 2θ_max/D dioptres
σ_centroid = σ_spot/√N, σ_spot = FWHM/2.355; wavefront noise σ_centroid·d/f
Sensitivity p·d/f per pixel; Strehl ≈ exp(−(2πσ/λ)²)
Dynamic range: the spot must stay inside its own sub-aperture (Akondi & Dubra, Opt. Express 29(6), 2021). Centroid noise is the photon-noise limit for a Gaussian of the spot's FWHM; read noise, background and pixelation add to it. Strehl by the extended Maréchal approximation (Mahajan, JOSA 73, 860, 1983).
Lenslets over the pupil (mm)
Spot size vs lenslet pitch
Centroid noise vs photons
Dynamic range vs sensitivity
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Diffraction-limited lenslet spots; dynamic range is the tilt at which a spot stays inside its own sub-aperture. Centroid noise is the photon limit for a Gaussian spot; read noise, background and pixelation are neglected. Maréchal's Strehl holds for S ≳ 0.3.
- Akondi V., Dubra A. (2021). Shack-Hartmann wavefront sensor optical dynamic range. Opt. Express 29, 8417. Eq. 2 (lenslet-bound dynamic range). doi:10.1364/oe.419311
- Mahajan V. N. (1983). Strehl ratio for primary aberrations in terms of their aberration variance. J. Opt. Soc. Am. 73, 860. Extended Maréchal approximation of the Strehl ratio. doi:10.1364/josa.73.000860