第１０章　繞射光學（Diffractive Optics）

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1 Diffractive Optics (Scalar Diffraction Analysis) 1.. extended scalar theory 1.3 Types of Diffractive Surface linear grating 1.3. Optical hologram Phase Model Paraxial properties and aberrations 1.4. f -θ Scan lens Achromatic doublets BK7/ infrared doublet eyepiece Surface relief kinoform ( )

2 L ( mv n' sinθ d nsinθ i = (1.1) L n n θ i θ d ν m θ i θ d θ i θ d 1.1 m ν ν ν 1..1 (Scalar Diffraction Analysis) Diffraction Grating yz y z= transmission function L 1-

3 t(y) t(y)=t(y+l) t(y) ( y) = Cm ( i mf y) t m= exp π 1. 1 f = Cm L C m = 1 L L t ( y) exp( i mf y) π dy 1.3 t(y) t(y) t(y) 1. z= z θ U planewave π, = 1.4 ν n ( y z ) = exp i y sinθ i Ut(y,z=) U t ( y, z = ) = U ( y, z = ) t( y) π = exp i y sinθ i ν n = = m= m= planewave C C m m m= C sinθ i exp iπy + mf ν n m sinθ d exp iπy ν n' exp i ( iπmf y) 1.5 (1.5) sinθ d sinθ i = + mf ν n' ν n 1.6 (1.6) C m 7 m m 7 m * 7 m CmCm = 1.7 (1.7) t(y) (1.) (1.5) (1.5) 1-3

4 (1.3) C m f (through put) (surface relief profile) kinoforms (y) Φ ( y ) α π y 1. t ( y) = exp[ iφ( y) ] sin ( πx) πx m [ π ( α m) ] [ π ( α m) ] sin η = = sin c ( α m) 1.8 sin c ( πx) argument sin c = ( ) 1 x sin c ( πx) = me 1.8 =1 η 1 =1. m= 1 surface-relief pattern OPD n'-n dy, dy π [ n' ( ) n( ) ] d( y) 1-4

5 d max d max d = max n' ( ) n( ) 1.9 n' n ~. 5 d max π φ max = [ n' ( ) n( ) ] d max 1.9 α ( ) [ n' ( ) n( ) ] [ n' ( ) n( )] = α ~ ( ) ηm ( ) = sin c m m= m=1 m= 1.3 η m max 1 η m = ηm ( ) d 1.1 max min min 1-5

6 max min 1.11 η m=1 m π η 1 1+ min max min min max + 3 a π ( + ) ( + ) max 1.13 min =, max = π η ~ binary Optics Φ ( y ) α π y 1.4 p p=4 η m1 p ( ) sin c m sin = p π p sin p [ π ( d m) ] ( d m) 1.15 p m=1 =1 = η 1.16 ( ) = sin c p 1, p N P= N N=4 P= 4 = P 1-6

7 π P P sin ( α m) ~ π ( [ α m )] P 1.15 η ( ) m m P ~ c c ( m p, sin sin α ) 1.17 m 1.17 sin c p sinc (d-m) 1.. extended scalar theory L L L Swanson Swanson 1 Swanson 1.5 surface profile 1 Swanson Binary Optics Technology: Theoretical Limits on Diffraction Efficiency of Multi level Diffractive Optical Elements", MIT, Lincoln Laboratory, Technical Report 914, 1 March

8 1.5 L θ i L transmission function απ t( y) = exp i y = L y L L y < L L L η m, ext = sin c α m 1.19 L L L = L L L L L duty cycle Swanson 1.19 OSLO Swanson optimum depth Snell m d opt 1-8

9 d opt = n n' m m L d opt L surface relief profile d L opt 1.9 OSLO d opt 1. Swanson Swanson L.5 L aspheric corrector L Swanson 1.3 Types of Diffractive Surface 1 constant-period OSLO OSLO 1-9

10 1.3.1 linear grating x y y substrate x y z= Rowland Rowland circle Concave grating Henry A. Rowland 188 Rowland Rowland Rowland 6 /mm 115mm OSLO grating spacing, GSP 1/6=.16mm Rowland 115/=57.5mm 1 8 3mm 3 4 dummy surface DRW ON Rowland Rowland 1-1

12 1.6 spot diagram 1.7 Rowland field aberration analysis yz Rowland 5 YFS= Optical hologram holographic optical element, HOE OSLO interference pattern Welford Opt. Commun W. T. Welford, "A vector raytracing equation for hologram lenses of arbitrary shape," Opt. Commun. 14, 3-33(1975) 1-1

13 OSLO len\demo\pro\hoe.len He-Ne.638 m 3mm prescription 1. HOE x,y HX1, HY1, HX, HY 1 z HZ1=-1. 1 HOE 1 HV1= 1 HZ=3 HOE HV=1 He-Ne Construction wavelength, HWV HWV=.638 reconstruction diffraction order, HOR HOR=-1 substrate HOE Welfold aplanatic element Abbe ray intercept curves Configuration1 Configuration 1-13

14 Phase Model CGH grating groove x,y x,y 1 1 x y f x = f y = L L f f x y ( x, y) ( x, y) 1 Φ = π x 1 Φ = π y ( x, y) ( x, y) x y

15 1.1 phase function OSLO axion-like Zernike Sweatt Sweatt Kleinhans n=1,1 n sweatt ( ) = [ nsweatt ( ) 1] Sweatt model C C 1 = C s = C s + φ [ n ( ) 1] sweatt φ [ n ( ) 1] sweatt 1.3 nominal power C s aspheric surface term OSLO SCP *dfrzswet *swetzdfr Sweatt model Paraxial properties and aberrations m=1 n OSLO DFR Φ π 4 6 () r = ( DF + PF1r + DFr + DF3r +K) 1.4 r 1.7 kinoform 1.4 ( ) π Φ r = j j DFO DFO= F1 t π () r = exp i DF r diff, parax

16 f π = πφ = t lens exp i r exp i r 1.6 f =1/f power = DF1 f r -1/f φ ( ) = φ Abbe diff bbort long ν diff = 1.8 short long 1.8 diff long > short diff< diff Abbe d, F, C ν diff ~ 3.45 achromatic achromatic achromat aphorized achromat DF1 4 DF Seidel 6 DF3 5 aspheric surface Sweatt n C 1 C Cs aperture stop distortion 1-16

17 Petzval Petzval Petzval Petzval 1/n n n Petzval 1.4. f -θ Scan lens f -θ 1 4 DF DF1 3 Petzval 4 stop Seidel f -θ Buralli Morris 3 - /3 35mm F F/ =.638 m ± Sweatt -f=-65mm n Sweatt OSLO n *swetdfr SCP DFR 3 D. A. Buralli and G. M. Morris, Design of diffractive singlets for monochromatic imaging, Appl. Opt. 3, (1991). 1-17

19 *spsopd SCP RMS RMS OPD menu Evaluate>>Spot Diagram>>Spot Sign and OPD V.S Field Petzval Sweatt f-θ *ftheta Scp 1-19

20 1.6 *swetzdfr Sweatt 1.7 show>>auxiliary Data>>Diffractive Surf Zone Achromatic doublets 1-

21 power r hybrid element ref diff = ref + diff ref diff Abbe φ φ ref diff ν ref = ν ν ref ν diff = ν ν diff diff ref φ φ 1.9 ref 1.9 Abbe Abbe 1.9 d, F C BK7 Abbe ref =64., diff = P diff = short short long 1.3 P diff partial dispersion d, F, C P diff =.596 longitudinal secondary color l ss 1 P = φ ν ref ref P ν diff diff 1.31 BK7/ achromat secondary spectrum.14 1/=.45 Spherochromatism fast system 1-1

22 1.4.4 BK7/ 1mm F F/7 BK7 ±

23 1.9 W. J. Smith Modern Lens Design public\len\wsmith\ch6 marginal transverse spherical aberration tangential coma f ray intercept curve Smith Fraunhofer Steinbeil 3 1-3

24 1.11 Conrady D-d Stone George infrared doublet /L chromatic properties Reidl McCann 5 Zinc Selenide Zinc Sulfide 3-5 m Amtir m Reidl McCann F/1 front surface r 4 T. Stone and N. George, Hybrid diffractive-refractive lenses and achromats, Appl. Opt. 7, (1988) 5 M. J. Reidl and J. T. McCann, Analysis and performance limits of diamond turned diffractive lenses for the 3-5 and 8-1 micrometer regions, Proc. SPIE, vol. CR38, (1991). 1-4

25 m 1-5

26 eyepiece Missig Morris 6 Missig Morris 5 Erfle 6 M. D. Missig and G. M. Morris, Diffractive optics applied to eyepiece design, Appl. Opt. 34, (1995). 1-6

27 1.13 Erfle 1/3 BK m /L /L =.58756/5=.3 /L 1.11 =.58756µm m=1 d, F, C integrate efficiency η η η int int 1 η int = A η pupil local pupil ( x, y) dxdy local 1.3 A pupil MTF Buralli Morris Appl. Opt. 31, (199) OSLO Swanson chief rays 1-7

28 1.14 /L kinoform

29 .58756µ m BK7 = 1.14µ m.5168 Kinoform Zone Kinoform blaze high 1.5 m kinoform MTF MTF 1-9

31 1-31

32 1-3

第三章單色差（monochromatic aberration）

第三章單色差（monochromatic aberration） monochromatic aberration.1...1 (The specification of ras).. (ra-intercept curves).. (comatic and astigmatic aberrations).. (defocusing)..5 (curvature of field and astigmatism)..6 (distortion). (aberration

第１０章 繞射光學（Diffractive Optics）

第１０章　繞射光學（Diffractive Optics）