Diffractive Optics 1.1 1. 1..1 (Scalar Diffraction Analysis) 1.. extended scalar theory 1.3 Types of Diffractive Surface 1.3.1 linear grating 1.3. Optical hologram 1.3.3 Phase Model 1.4 1.4.1 Paraxial properties and aberrations 1.4. f -θ Scan lens 1.4.3 Achromatic doublets 1.4.4 BK7/ 1.4.5 infrared doublet 1.4.6 eyepiece 1.1 1.. 3. 4. 5. Surface relief kinoform ( ) 1. 1-1
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-
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
(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
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( )] = 1.1 1.1 α ~ ( ) ηm ( ) = sin c m 1.11 1.11 1.3 m= m=1 m= 1.3 η m max 1 η m = ηm ( ) d 1.1 max min min 1-5
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 = + 1.13 π η ~1 6 1.14 4 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 1.15 1.8 m=1 =1 = 1.5 1 η 1.16 ( ) = sin c p 1, p N P= N N=4 P= 4 =16 1.16 98.7 P 1-6
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 1991. 1-7
1.5 L θ i L transmission function απ t( y) = exp i y = L y L L y < L 1.18 1.3 L L η m, ext = sin c α m 1.19 L L L = 1 1.19 1.8 L L L L L duty cycle Swanson 1.19 OSLO Swanson optimum depth Snell m d opt 1-8
d opt = n n' m m L 1. 1. 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
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
1.1 1.6 1-11
1.6 spot diagram 1.7 Rowland field aberration analysis yz Rowland 5 YFS= 1.7 1.3. 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
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
1.8 1.3.3 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 1.1 1-14
1.1 phase function OSLO axion-like Zernike Sweatt Sweatt Kleinhans n=1,1 n sweatt ( ) = [ nsweatt ( ) 1] + 1 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 1.4 1.4.1 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 1 1.5 1-15
f π = πφ = t lens exp i r exp i r 1.6 f =1/f power 1.5 1.6 1 = DF1 f r -1/f φ ( ) = φ 1.7 1.7 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
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 ± 16 8.5 11 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, 151-158 (1991). 1-17
1.4 1.1 1.1 1-18
*spsopd SCP RMS RMS OPD menu Evaluate>>Spot Diagram>>Spot Sign and OPD V.S Field 1.11 1.11 5 Petzval Sweatt 1.5 1.5 f-θ *ftheta Scp 1-19
1.6 *swetzdfr Sweatt 1.7 show>>auxiliary Data>>Diffractive Surf Zone 18 1.4.3 Achromatic doublets 1-
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 =-3.45 95 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
1.4.4 BK7/ 1mm F F/7 BK7 ±1 3 4 6 95 5 1.8 1.9 1-
1.9 W. J. Smith Modern Lens Design public\len\wsmith\ch6 marginal transverse spherical aberration tangential coma f 1.1 1 ray intercept curve Smith 6. 6.3 Fraunhofer Steinbeil 3 1-3
1.11 Conrady D-d Stone George 4 1.4.5 infrared doublet /L chromatic properties Reidl McCann 5 Zinc Selenide Zinc Sulfide 3-5 m Amtir 3 8-1 m Reidl McCann F/1 front surface r 4 T. Stone and N. George, Hybrid diffractive-refractive lenses and achromats, Appl. Opt. 7, 96-971(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, 153-163 (1991). 1-4
1.11 8-1 m 1-5
1.1 1.1 1.4.6 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, 45-461 (1995). 1-6
1.13 Erfle 1/3 BK7 36 5 m /L /L =.58756/5=.3 /L 1.11 =.58756µm m=1 d, F, C 1..865.964 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, 4389-4396 (199) OSLO Swanson chief rays 1-7
1.14 /L kinoform 1. 1-8
.58756µ m BK7 = 1.14µ m.5168 Kinoform Zone Kinoform blaze high 1.5 m 7 1.15 kinoform 99.5 87. 95.6 MTF MTF 1-9
1.16 1-3
1-31
1-3