Topic 10: Applications of Holography Aim: To review a range of - PDF document

E I H T Y T Modern Optics O H F G R E U D B I N Topic 10: Applications of Holography Aim: To review a range of applications of holography, including holo- graphic lenses and commercial holographic applications. Contents: � Holographic Lens � Variations on Holographic Lens � Hologon � Head-Up display P T O I C D S E G I R L O P P U A P D S Applications of Holographic -1- Autumn Term C E P I S A Y R H T P M E o f N T

E I H T Y T Modern Optics O H F G R E U D B I N Holographic Lens Consider a hologram made with a plane beam reference and a point source object. z Beamsplitter oint Source Po Reference Beam Then at P 0 the object wave is ( ı Φ ( x ; y )) ( x ; y ) exp = Ah ( x ; y ; z ) o ( x ; y ; z ) is the Free Space Response Function . where h The reference wave is perpendicular to the plate, so is just r exp ( Φ 0 ) = Constant Taking the Fresnel Approximation we have that = λ exp ( ı κ z ) ı κ � � ( x 2 + y 2 ( x ; y ; z ) ) h exp ız 2 z so that the object wave is, ( x 2 + y 2 � � �� ) ı κ + o 0 exp z 2 z where = A λ o 0 ız P T O I C D S E G I R L O P P U A P D S Applications of Holographic -2- Autumn Term C E P I S A Y R H T P M E o f N T

E I H T Y T Modern Optics O H F G R E U D B I N The intensity in plane P 0 is then, 2 � ( x 2 + y 2 � � � ) � � ( Φ 0 ı κ � � ( x ; y ) = ) + O 0 exp + g � r exp z � � 2 z � which, with some re-arrangement, gives + x 2 + y 2 � � � � κ Φ 0 r 2 j 2 + j O 0 + 2 rO 0 cos z 2 z Now if we assume that, κ z = Φ 0 � 2 n π then the intensity pattern can be simplified to give, κ x 2 + y 2 � � r 2 j 2 + j O 0 + 2 rO 0 cos 2 z Which is the equation of a set of circular fringes with a bright fringe when κρ 2 = 2 n π ρ 2 = x 2 + y 2 where 2 z or the radius of the n th fringe is given by ρ n p 2 n λ z = This is Just Newton’s Rings P T O I C D S E G I R L O P P U A P D S Applications of Holographic -3- Autumn Term C E P I S A Y R H T P M E o f N T

E I H T Y T Modern Optics O H F G R E U D B I N Holographic Reconstruction Form hologram as previous with + δ ˆ ( x ; y ) = g 0 ( 1 g ( x ; y )) g with, in this case κ x 2 + y 2 � � = 2 rO 0 δ ˆ g ( x ; y ) cos 2 z g 0 Expose hologram and develop to get Amplitude Transmittance, � a δ ˆ ( δ ˆ ) 2 = T 0 + b T a g g Reconstruct with Collimated Beam = r exp ( ı Φ 0 Let Φ 0 ( x ; y ) ) = 0 u then the transmitted amplitude is v ( x ; y ) = rT a = 0 1) First Two Terms Let b We can expand to get Three terms, v ( x ; y ) = + rT 0 (1) � ı κ ar 2 O 0 � � ( x 2 + y 2 ) + exp (2) g 0 2 z ı κ ar 2 O 0 � � ( x 2 + y 2 ) exp (3) g 0 2 z P T O I C D S E G I R L O P P U A P D S Applications of Holographic -4- Autumn Term C E P I S A Y R H T P M E o f N T

E I H T Y T Modern Optics O H F G R E U D B I N which give 1. Partially transmitted DC beam 2. Lens of focal length z � z 3. Lens of focal length Virtual Focus Focus Hologram Transmitted Beam z z Very similar to a Zone Plate. See tutorial on Zone Plate for comparison. P T O I C D S E G I R L O P P U A P D S Applications of Holographic -5- Autumn Term C E P I S A Y R H T P M E o f N T

E I H T Y T Modern Optics O H F G R E U D B I N 6 = 0 2) Add non-linear Term b Then we get Three extra terms, br 3 O 2 0 + (4) g 2 0 � ı κ br 3 O 2 � � ( x 2 + y 2 0 ) exp (5) g 2 z o ı κ br 3 O 2 � � 0 ( x 2 + y 2 = ) exp (6) g 2 z 0 which give 1. Extra transmitted DC beam. 2. Lens of focal length z = 2 � z = 2 3. Lens of focal length Virtual Foci Foci Hologram Transmitted Beam z z z/2 z/2 Problem with overlapping orders P T O I C D S E G I R L O P P U A P D S Applications of Holographic -6- Autumn Term C E P I S A Y R H T P M E o f N T

E I H T Y T Modern Optics O H F G R E U D B I N Variations of Holographic Lens. Change the formation geometry, (move off-axis). Reference Beam Po Object When we reconstruct we then get, Hologram Reconstruction DC Beam Beam Virtual Foci Real Foci With the order separated, and useful foci (both real and virtual). Note with holographic lenses. � Reconstruction work equally well in Kirchhoff region, so able to form very wide aperture systems. � Bleach lenses to get diffraction efficiency of � 33% � Only works in monochromatic light P T O I C D S E G I R L O P P U A P D S Applications of Holographic -7- Autumn Term C E P I S A Y R H T P M E o f N T

E I H T Y T Modern Optics O H F G R E U D B I N Thick Holographic Lenses Make reflection, Thick Hologram with object and reference beam from] opposite sides Converging Object Wave Reference Beam Thick Holographic Material When we reconstruct we then get, Bragg Planes Reconstruction Beam Single Reflection Focus We can get single focus with efficiency up to 90%. Very useful technique to produce wide aperture lenses for compact optical systems, (still monochromatic ONL Y). Major Potential: Make holographic lens in red light, then swell gelatin to reconstruct in the Infra-Red where it is difficult to make lenses. (considerable potential) P T O I C D S E G I R L O P P U A P D S Applications of Holographic -8- Autumn Term C E P I S A Y R H T P M E o f N T

E I H T Y T Modern Optics O H F G R E U D B I N Practical Systems. 1) The Hologon: Consider forming a grating of the type, d0 d1 Then the diffraction angle will be given by = λ sin θ d ! d 1 across the grating. where d varies between d 0 Illuminate this with a scanning beam, Angle of scan Variable Scanning Beam θ Grating 1 θ 0 Angle of the diffracted scan is given by the grating spacing variation. P T O I C D S E G I R L O P P U A P D S Applications of Holographic -9- Autumn Term C E P I S A Y R H T P M E o f N T

E I H T Y T Modern Optics O H F G R E U D B I N Make “wheel” containing a range of these gratings at different angles, Various Gratings Then assemble the whole systems as Rotate Slowly Rotate Fast Output Pattern The output scan speed is determined by the speed of the rotating hexagonal prism and the orientation by the sector of the Hologon. P T O I C D S E G I R L O P P U A P D S Applications of Holographic -10- Autumn Term C E P I S A Y R H T P M E o f N T

E I H T Y T Modern Optics O H F G R E U D B I N System is the basis of the Automatic Bar-Code reader. Scanning Beam Measure the Reflected Light , and we get I(t) t Reflected light then analysed to “read” the 12 digit bar-code. The largest use of holograms Actual holograms and optics make-up a significant part of the cost of a supermarket check-out. P T O I C D S E G I R L O P P U A P D S Applications of Holographic -11- Autumn Term C E P I S A Y R H T P M E o f N T

E I H T Y T Modern Optics O H F G R E U D B I N Head-Up Displays Used mainly in military aircraft as in-flight projection system. Glass Canopy From Distant Objects Projected Flight Information Aim: Project instruments (and target) information into pilots field of view. 1): Semi-Silvered Mirror: Old system, with many problems, 1. Light loss from distant objects 2. Reflection too dim 3. Reflections from inside canopy 4. Very small angle of view, and sever distortions P T O I C D S E G I R L O P P U A P D S Applications of Holographic -12- Autumn Term C E P I S A Y R H T P M E o f N T

E I H T Y T Modern Optics O H F G R E U D B I N 2): Holographic Filter: Use volume hologram to reflect at wavelength to match instruments. Typical filter: � External Transmittance 97% except about selective wavelength. (5nm region lost) � Instrument Illumination 95% reflectivity about selected wave- length (typically 530nm). White Light White Light - 530nm Plus (From outside) Light from Instruments From Instruments Holographic Grating (530 nm) This “flat” holographic filter removes the light efficiency problems, but not the movement problems. P T O I C D S E G I R L O P P U A P D S Applications of Holographic -13- Autumn Term C E P I S A Y R H T P M E o f N T