Streamlined Diffraction Corrections in Practical Radiometry. Eric Shirley, Simon Kaplan, Solomon Woods Sensor Science Division (NIST)

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$Streamlined Diffraction Corrections in$ Kaplan, Solomon Woods Sensor Science Division

1 Streamlined Diffraction Corrections in Practical Radiometry Eric Shirley, Simon Kaplan, Solomon Woods Sensor Science Division (NIST) Adriaan Carter, Timothy Jung Jung Research and Development

2 Generic unfolded optical system:

3 Generic unfolded optical system: Kirchhoff s treatment applied iteratively: Integration over Optical surface areas Free-space Scalar wave propagator (focusing effects)

4 Generic unfolded optical system: SAD (source-aperture-detector) Paradigm: Treat diffraction piecewise via effective 3-element subsystems J. Opt. Soc. Am. A 33(8), 1509 (2016)

5 Generic unfolded optical system: SAD (source-aperture-detector) paradigm: Treat diffraction piecewise via Effective 3-element subsystems THIS PRESENTATION: (1.) Progress in the SAD problem (2.) Example of a BB calibration scenario SAD-compatible effects Other 1-edge effects Major 2-edge effects (3.) Radiance-mode calibration (3.) measurements

$v0 max( vs, vd) min( v, v ) / v v 0 0 3 4 2 2 2 2 2 4 a s d / ( s d0 ) 2 2 2 1/2 C R R R d d G(, x) {(1 x )[(2 x) ]} / (1 x) 1 1 ( ) CL ( ) dx G(, x) L( u, v (1 x)) s d 0 Wolf s formula for fraction$

6 Source-Aperture-Detector (SAD) Paradigm/Geometry Three dimensionless parameters: v (2 R R / ) / d s s a s v (2 R R / ) / d d d a d 2 a s d u (2 R / )(1/ d 1/ d 1/ f ) Treatment of extended sources: v0 max( vs, vd) min( v, v ) / v v a s d / ( s d0 ) /2 C R R R d d G(, x) {(1 x )[(2 x) ]} / (1 x) 1 1 ( ) CL ( ) dx G(, x) L( u, v (1 x)) s d 0 Wolf s formula for fraction of point source s flux falling on aperture that reaches detector. 0

7 To evaluate 1 1 ( ) CL ( ) dx G(, x) L( u, v (1 x)) 0 From Wolf we have L( u, v) 1 L ( v, w) 2 B L( u, v) w [1 L ( v, w)] L ( v, w) Thermal total power case: B X A c 2 / ( T) v c1 6 (4) L( u, v) 0 d L( u, v) L ( ) F (, ) 4 4 B A w A c1 2 6 (4) L( u, v) 0 d L( u, v) L ( ) w F (, ) (, ) 4 4 B A w FX A w A

8 Lovely (and practical!) asymptotic expansions for relevant quantities L B 1 2 cos(2 v) 1 20w 90w 20w w ( v, w) ~ 2 v(1 w ) v (1 w ) 4v (1 w ) (1 18 w w ) sin(2 v)... 4 v (1 w ) (3) e FB ( Aw, )~ (1 w ) 4 (1 w ) 2 6 (1 w ) ( 1 w ) 1 w w 90w 20w w 1 2 6log 2 11/ 3 1 5w 112w 586w 112w 5 32 w (1 w ) 1 w 1 A A log log e A A e A With palindromic polynomials at all orders, as well as in L X (v,w) and F X (A,w). Small-wavelength, asymptotic form for spectral power for extended sources: Limiting case: Non-limiting case: All a functions involve phased exponentials times smooth functions of wavelength, facilitating interpolation!

9 Beyond the SAD paradigm: Multistage optics trains Vignetting effects

10 Beyond the SAD paradigm: Multistage optics trains Vignetting effects One-edge effects corrections or 1/T. Length of two-segment path involving one edge point = stationary

11 Beyond the SAD paradigm: Multistage optics trains Vignetting effects One-edge effects corrections or 1/T Two-edge effects corrections 2 or 1/T 2 esp. for baffle+pinhole SAAD case Length of three-segment path involving two edge points = stationary

12 Beyond the SAD paradigm: Multistage optics trains Vignetting effects One-edge effects: corrections proportional to or 1/T. Two-edge effects (most important for source-pinhole-baffle-detector cases): corrections proportional to 2 or 1/T 2. Example: blackbody calibration in NIST s Low-background infrared facility:

13 Beyond the SAD paradigm: Multi-stage optics trains Vignetting effects One-edge effects: corrections proportional to or 1/T. Two-edge effects (most important for source-pinhole-baffle-detector cases): corrections proportional to 2 or 1/T 2. EFFECT ON TOTAL POWER: (4) (6) (4) (5) 2 (4) (5) (6) loss ( ) gain ( ) gain ( ) [ f1 f1 ] [ f2 f2 2 F( ) F F F f ].

14 SAD subsystems-- (4) (6) (4) (5) 2 (4) (5) (6) loss ( ) gain ( ) gain ( ) [ f1 f1 ] [ f2 f2 2 F( ) F F F f ].

15 SAD subsystems-- (4) (6) (4) (5) 2 (4) (5) (6) loss ( ) gain ( ) gain ( ) [ f1 f1 ] [ f2 f2 2 F( ) F F F f ].

16 SAD subsystems-- (4) (6) (4) (5) 2 (4) (5) (6) loss ( ) gain ( ) gain ( ) [ f1 f1 ] [ f2 f2 2 F( ) F F F f ].

17 Further 1-edge effects-- (4) (6) (4) (5) 2 (4) (5) (6) loss ( ) gain ( ) gain ( ) [ f1 f1 ] [ f2 f2 2 F( ) F F F f ].

18 Further 1-edge effects-- (4) (6) (4) (5) 2 (4) (5) (6) loss ( ) gain ( ) gain ( ) [ f1 f1 ] [ f2 f2 2 F( ) F F F f ].

19 Main 2-edge effects-- (4) (6) (4) (5) 2 (4) (5) (6) loss ( ) gain ( ) gain ( ) [ f1 f1 ] [ f2 f2 2 F( ) F F F f ].

20 Main 2-edge effects-- (4) (6) (4) (5) 2 (4) (5) (6) loss ( ) gain ( ) gain ( ) [ f1 f1 ] [ f2 f2 2 F( ) F F F f ].

21 Main 2-edge effects-- (4) (6) (4) (5) 2 (4) (5) (6) loss ( ) gain ( ) gain ( ) [ f1 f1 ] [ f2 f2 2 F( ) F F F f ].

22 Example s overall diffraction effects on spectral power:

23 Error obtained using SAD-compatible-only effects: (4) (6) (4) (5) 2 (4) (5) (6) loss ( ) gain ( ) gain ( ) [ f1 f1 ] [ f2 f2 2 F( ) F F F f ]. Error, red only

24 Error including SAD + other 1-edge effects: (4) (6) (4) (5) 2 (4) (5) (6) loss ( ) gain ( ) gain ( ) [ f1 f1 ] [ f2 f2 2 F( ) F F F f ]. Error, red only Error, w/ + 1 corr.

25 Error including SAD + other 1-edge effects + dominant 2-edge effects: (4) (6) (4) (5) 2 (4) (5) (6) loss ( ) gain ( ) gain ( ) [ f1 f1 ] [ f2 f2 2 F( ) F F F f ]. Error, red only with + 1 corr. with corr.

26 Spectrally integrated result vs. T (shown as Blevin s effective wavelength):

27 Treating radiance-mode calibration by a standard radiometer (MDXR) viewing A Lambertian source. Sample results: Total diffraction effect involves two SAD-type factors. Two MDXR configurations: BIB: SAD=pupil, spatial filter, filter-holder ACR: SAD=pupil, spatial filter, ACR entrance Two source possibilities: LSPS: A notional collimator chamber, SAD=BB, aperture, MDXR pupil FLOOD: A wide-mouth BB flood source SAD=BB, aperture, MDXR pupil

28 THIS PRESENTATION: (1.) Progress in the SAD problem (2.) Example of a BB calibration scenario SAD-compatible effects Other 1-edge effects Major 2-edge effects (3.) Radiance-mode calibration measurements Thank you for your attention!

Electro-Optical System. Analysis and Design. A Radiometry Perspective. Cornelius J. Willers SPIE PRESS. Bellingham, Washington USA

Electro-Optical System. Analysis and Design. A Radiometry Perspective. Cornelius J. Willers SPIE PRESS. Bellingham, Washington USA Electro-Optical System Analysis and Design A Radiometry Perspective Cornelius J Willers SPIE PRESS Bellingham, Washington USA Nomenclature xvii Preface xxiii 1 Electro-Optical System Design 1 11 Introduction