Design of 10X zoom system by diffractive-refractive hybrid lens A Thesis Submitted to Institute of Electro-Optical Engineering College of Electronic E

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2 Design of 10X zoom system by diffractive-refractive hybrid lens A Thesis Submitted to Institute of Electro-Optical Engineering College of Electronic Engineering and Computer Science National Chiao Tung University In partial Fulfillment of the Requirements For the Degree of Master In Electro-Optical Engineering July 004 Hsinchu, Taiwan, Republic of China

Science National Chiao Tung University In partial Fulfillment of the Requirements For

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4 Design of 10X zoom system by diffractive-refractive hybrid lens Student Yi-Chen Lu AdvisorProf. Mao-Hong Lu Institute of Electro-Optical Engineering National Chiao-Tung University Abstract This thesis contains two parts. In the first part, we design a 10X zoom lenses which can be used camera system. The diffractive lens is characteristic of thinness and lightness, and costs effectively. The diffractive lens has the same imaging function as refractive lens. The hybrid lens which contains the diffractive lens formed on a surface of refractive lens can eliminate more aberrations, and decrease the volume and weight. With the advantage of the diffractive device, we accomplish the compact 10X zoom system which is made of four hybrid-aspheric lenses and two spherical lenses. In the second part, we measure the optical performances of a 3X zoom lens made of hybrid lenses. From the measured results, we find that for a hybrid system (including diffractive components) the centering, aligning and packaging are required to be made more accurately than a pure refractive system in order to get good performance. II

$In the first part, we design a 10X zoom lenses which can be used camera system. The diffractive lens is characteristic of thinness and lightness, and costs effectively.$

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18 ρ Rb = kλ k ρ R + b 1 ( k N ) k = = ρ 1 Rbλ R + b R Mk θk Mk-1 ρk rk rk-1 S O b P G ρ k ρ k k π π 7

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20 λ 5 iφ ( x, y) t( x, y) = e, ) A i φ( x y i e iφ 0 ( x, y) iφi ( x, y) i( φ + φi ) A e = t A e = A e 0 i i φ ( x, y) = φi ( x, y) + φ( x, ) 0 y φ( x, y) = φ0( x, y) φ ( x, y) i 9

21 π φ( x, y) = λ 0 m, n a mn x m y n π n φ(, y ) = a r n x λ0 n [ ] 0,π π [ φ ] mod π Ψ x, y) = ( x, y) + φ ( 0 φ0 λ0 Ψ( x, y) λ h( x, y) = n( ) 1 π 0 λ 0 λ n( λ ) 1 0 ( x, y) = h m 0 π φ 0 π 10

22 11 ), ( y x Ψ = ) ( h P h P h P h P h φ

23 Sag ( h) h = ( 1+ K ) h r 1+ 1 r A h + A h + A h + A +L h N ( N ) ( N ) h i h c ( N ) ( h i N ) ( N ) ( N ) π h 0 N h i ( N ) ( N ) h c h 0 h 0 1

24 π( N 0.5) = P h i o ( N ) + P h ( N ) + P h ( N ) + P h ( N ) + L 4 i 6 i ( N ) + P h ( N ) + P h ( N ) + P h ( ) + L π( N + 0.5) = P h N 4 o 6 o 8 8 i o H N ( H h N ) d ( ) Num N h = o ( N ) h ( N ) H d i Num( N ) = fix[ Num( N )] + 1 H h ( N ) h = o ( N ) hi ( N ) Num( N ) ( Num N ) N fix N h N ( n ; N ) h ( n ; N ) = hi ( N ) + ( n 1) Hh ( N ) N [ ] n = 1,, 3, L, Num( N ) + 1 N h N ( n ; N ) X S ( n ; N ) X A S ( n ; N ) ( n ; N ) hn = (1+ K) h r 1+ 1 r N ( n ; N ) hn ( n ; N ) + A6 hn ( n ; N ) + A8 hn ( n ; N ) + L 13

25 X α α ( n ; N ) = tan 1 dx dh S N ( n ; N ) ( n ; N ) 14

26 t 1λ t ( n ; N ) = n o cosθ o λ n1 cosθ 1 n o n θ o θ 1 t 1 ( n ; N ) = t( n ; N )/ cos[ ( n N )] X ; 1λ α X X ( n N ) = X ( n ; N ) ; 1λ ( h ) φ π N N 15

27 ( n ; N ) = X ( n ; N ) + X ( n N ) X S ; r r r Z Z Z S L Z (a) (b) (c) kinoform 16

28 1 1 3 W S + hρ cosθ S+ ρ cos θ h ρ (S+S)+ h 3 ρ cosθ 4 4 ( h. ρ, cosθ ) = ρ 1 h S+ S u u u u y u u h 17

29 c B= c 1 1 C= + c c u + u' u u' c )(n-1) ϕ =( 1 c y S = 4 4 ϕ 3 n n + 4( n + 1) 3n + ( ) + B + BC + C n 1 n( n 1) n( n 1) n S= 3 y ϕ H n + 1 n + 1 B + C n( n 1) n S=H ϕ S H ϕ n = 18

30 19 1 ) 1)( ( = + = = + = n B c c n c c c c c T s ϕ ϕ ] 3 4 [1 4 Gy m C TC T y λ ϕ = / ) ( C T H y + = ϕ ϕ H = 0 = 0 = tu y =

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33 ϕ = ( n 1) C ϕ = Kλ n1 1 λ1 V = > 0 V = < 0 n n λ λ P n n 3 n n 1 3 = 3 λ P = λ 1 3 λ λ 3 3 λ 3 > λ1 > λ V d

34 ϕ = ( λ) ϕ ( λ) ϕ ( λ) hyb ref + dif 3

35 1 f ' 1 f dif F dif 1 f ' ref 1 = F' + 1 f F ref 1 = f C dif 1 + f + c ref F f dif f ref f ' f ' dif ref Vdif Vref = F'( ) V dif Vref Vdif = F'( ) V ref 4

36 P n n λ1 λ λ = 1λ n f n c P λ λ λ λ 1 1 λ λ = f c P λ 1 λ 5

37 l P = f ' V a λ a d P V b λ F F ' λ F b d l λ F f i P λ F i i V i i d 6

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39 1 f 1 f β f f = f 1 β f 1 f β 1 F 1 F 8

40 β 1 l 1 l 1 = l 1 l = l1 l β = 1 β l β1 l ' 1 1 l ' 1 β l l' β l β 1 β 1 M β β 1 9

41 β 1 β = 1 1 β = β 1 1 L = l l = f f = f 1 ( ) 4 β L β = l l = ( f L β + x ) ( f + x) f = ( f βf ) ( f ) = ( β β 1 ) β f = f = m l + x l f + x f x = = x f 1 β 1 L + + f 1 β ( β ) β = L L = β 30

42 β = 1 ß = 0 ß <<1 ß >>1 ß = ß = 0 β << 1 β >> 1 β = 31

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103 1., ( / ) 1997, Kleinhans W A. Aberration of curved zone plates and fresnel lenses Appl. Opt., 1997, 16: 1701~1704 Stone T, George N. Hybrid diffractive-refractive lenses and achromats Appl. Opt.,1988, 7(14):96 7. Shin-ichi, Mihara,VARI-FOCAL LENS SYSTEM United States Patent, Num:4,818,083(1989) 8. Kazuo Tanaka,ZOOM LENSUnited States Patent, Num:4,859,04(1989) 9. Hiroyuki Hamano, Kenichi Kimura, Saburo Sugawara,REAR FOCUS TYPE ZOOM LENSUnited States Patent, Num:5,134,54(199) 10. Hironori Shibata, Astujiro Ishii,WIDE-ANGLE ZOOM LENS SYSTEM HAVING A HIGH VARIFOCAL RATIO United States Patent, Num:5,418,646(1995) 11. Tetsuo Nagata, Hachioji,ZOOM LENS SYSTEM USING A DIFFRACTIVE OPTICAL ELEMENT AND IMAGE PICKUP DEVICE USING THE SAME United States Patent, Num:6,157,494(000) 1. Robert E. Fischer, Biljana Tadic-Galeb,Optical System Design McGraw-Hill Companies, , / 003, 14. Stenfan Sinzinger, Jurgen Jahns, Microoptics, WILEY-VCH, 1999 Shinchi Mihara, COMPACT REAR FOCUSING ZOOM LENS United States Patent, Num:5,808,810(1998), 1996, 17. ZEMAX User's Guide, Version 9.0 9

苗栗三山國王信仰及其地方社會意涵 The Influences and Implications of Local Societies to Three Mountain Kings Belief, in Taiwan Miaoli 研究生 : 林永恩指導

苗栗三山國王信仰及其地方社會意涵 The Influences and Implications of Local Societies to Three Mountain Kings Belief, in Taiwan Miaoli 研究生 : 林永恩指導國立交通大學客家文化學院客家社會與文化學程碩士論文苗栗三山國王信仰及其地方社會意涵 The Influences and Implications of Local Societies to Three Mountain Kings Belief, in Taiwan Miaoli 研究生 : 林永恩指導教