Analysis of Systematic Effects in 0/45 Lamp-plaque Sensor Calibration

Transcription

1 Analysis of Systematic Effects in 0/45 Lamp-plaque Sensor Calibration Leonard Hanssen,* Eric Shirley, Heather Patrick, Thomas Germer, David Allen, B. Carol Johnson, Howard Yoon NIST CALCON 2017 SDL/USU Logan, UT August 2017 * Presenter

2 The 0/45 concept: Irradiance-calibrated lamp source (FEL) 0/45 BRDF-calibrated diffuse plaque (usu. PTFE) Known radiance presented to unit under test (UUT) Diffusely scattering plaque (x,y,z) Radiometric analysis could include Lamp irradiance or intensity vs. distance Lamp intensity vs. direction BRDF variation when not in 0/45 configuration Polarization effects Spectral aspects Plaque uniformity (position, azimuthal, flatness) UUT 45 deg z This talk: Lamp properties BRDF variation Comparison of lamp-plaque and integrating-sphere source (ISS) measured by an imager FEL

3 PTFE Plaque

4 PTFE Plaque n

5 Geometrical notation at the plaque: n ẑ ŷ ˆx

6 Geometrical notation at the plaque: Angle of incidence: θ i Direction of incidence: q = c xˆ+ c yˆ c zˆ i xi yi zi ẑ n q i θ i ˆx ŷ

7 Geometrical notation at the plaque: n θ i Angle of incidence: θ i Direction of incidence: q = c xˆ+ c yˆ c zˆ i xi yi zi ẑ q i θ s q s Angle of scatter: θ s Direction of scatter: q = c xˆ+ c yˆ+ c zˆ s xs ys zs ˆx ŷ

8 Geometrical notation at the plaque: n θ i Angle of incidence: θ i Direction of incidence: q = c xˆ+ c yˆ c zˆ i xi yi zi ẑ q i θ s q s Angle of scatter: θ s Direction of scatter: q = c xˆ+ c yˆ+ c zˆ s xs ys zs ˆx ŷ φ r Relative azimuthal angle: φ r

9 Parametrization of ratio: Expansion about 0/45 configuration (2.) Use a low-order polynomial: BRDF( θ, θ, φ ) i s r BRDF(0,45, ) (1.) Introduce 3 small parameters = sinθ sin(45 ) µν 2 xi yi xs ys i s s µν i s t s µ = 0,1,2, ν = 0,1,2 = gc (, c ; c, c ) = hl (, l, t ) = 1+ c l l + ct + l t l s = sin sin θ s cos i i r = θ sin φ φ s i r

10 Spectral tri-function automated reference Reflectometer (STARR) Catherine C. Cooksey In-plane BRDF (φ r =0 or 180 ) Variable θ i, θ r Directional/hemispherical 250 nm to 2500 nm Goniometric optical scatter instrument (GOSI) Thomas A. Germer, Heather Patrick Full BRDF, laser-based (Si region) Includes out-of-plane Future: ROSI (Robotic Optical Scatter Instrument), which is slated to take on STARR capabilities for customers, with full BRDF Heather Patrick

11 Parametrization of ratio BRDF( θi, θs, φr) µν 2 = gc ( xi, cyi ; cxs, cys) = 1+ cµν li ls + ct t s + BRDF(0,45, ) µ = 0,1,2, ν = 0,1,2 g(c xi,0;c xs,0) c µυ from legacy STARR data g(cos(45 ),0;c xs, c ys ) c t from GOSI data GOSI STARR c xs c ys c xs 0.3

12 But, Exyz (,, ; λ ) =? Plaque, calibrated for BDRF (x,y,z) Distance from geometric center of FEL coils UUT 45 deg z Effective distance 2 2 1/2 r = [ x + ( z cm) ] eff = ( 0.1 cm) + d r y Distance from radiometric center of FEL coils FEL, calibrated for irradiance at 50 cm distance

13 Lamp cal: FASCAL-2 (50 cm, on axis) Distance effect: uniformity test [Yoon et al., Proc. SPIE 8510, 85100D (2012)] 2 = deff Ixyz (,, ) Ecal ( λ) dcal cm I(0, 0, z) i GSF Exyz (,, ; λ ) cos θ Validation of 1/r 2 law presented by Yoon et al. Angular effects on intensity: Gonio Spectroradiometer Facility (GSF, Yuqin Zong) 361 directions: -9 deg lat. To +9 deg lat. -9 deg long. to +9 deg long. Relative intensity Polarization aspects: 2.5 % polarized, tipped about 10 (like coils of large helix towards the viewer.) Ellipse exaggerates anisotropy. Plaque reduces polarization Total flux barely affected. Note: spectral effects are weak. K.J. Voss and L.B. da Costa, Appl. Opt. 55 (31) 8829 (2016).

14 Conceptual framework for demonstration experiment-- UNIT UNDER TEST (UUT): Angle dispersion FPA (2D) Angle dispersion Slit (1D) Pupil, maps angles on slit (focus= ) Pixel FOV= ˆω ˆω Radiant surface or scene Offner-type spectrometer Footprint of pupil (in cylinder along given direction)

15 Power delivered to pixel for integrating-sphere source (ISS) & lamp/plaque cases: ISS case Φ = dω A cos sec L cos λ θ θ θ UUT Pixel s ISS s PUPIL [ ] ωˆ θ s ˆn Lamp/plaque case Pixel FOV d ISS wall or plaque area enclosed In cylinder A cos Cosine factor (projected UUT pupil area) sec Φ = ω λ θ θ UUT Pixel s PUPIL ISS radiance, cosine factor { E g(...) BRDF(0 / 45) cosθ } λ Irradiance in FOV, g-factor, BRDF, cosine factor s θ s ˆn ωˆ

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19 Various effects on signal in lamp-plaque case: g 1/r 3 FEL intensity variation Total

20 Conclusions Lamp/plaque introduces effects in sensor calibrations that differ from those of integrating spheres The effects can depend on the lamp Optics of sensors (e.g., working distance) may need to be known Further work is needed to finalize quantitative analysis