Holographic method and apparatus using incoherent light

Claim 1

A method of generating a quasi-complex hologram using incoherent light and a conoscope system comprising a birefrigerant crystal inserted between two circular polarizers, the method comprising the following steps: (i) recording a plurality of different conoscopic holograms of the same object without relative displacement thereof and with respective different polarization configurations; (ii) digitizing said plurality of different conoscopic holograms to form a plurality of digital signals, each corresponding to one of said different conoscopic holograms, and (iii) combining by calculation in an arithmetic processor the various digital signals corresponding to the different conoscopic holograms obtained in this way in order to remove the bias and the conjugate image.

Claim 2

A method of generating a quasi-complex hologram using incoherent light and a conoscope system comprising a birefrigerant crystal inserted between two circular polarizers, the method comprising the following steps: (i) recording a plurality of different conoscopic holograms of the same object without relative displacement thereof and with respective different polarization configurations; (ii) digitizing said plurality of different conoscopic holograms to form a plurality of digital signals, each corresponding to one of said different conoscopic holograms, and (iii) combining by calculation in an arithmetic processor the various digital signals corresponding to the different conoscopic holograms obtained in this way in order to remove the bias and the conjugate image.

Claim 18

A method of generating a quasi-complex hologram using incoherent light and a conoscopic system comprising a birefrigerant crystal inserted between two circular polarizers, the method comprising the following steps: (i) recording four conoscopic holograms of the same object without relative displacement thereof in the following respective different polarization configurations with circular polarizers constituted by respective linear polarizers and respective quaterwave plates capable of relative rotation: α.sub.a =α.sub.b =+/-π/4 (1) α.sub.a =-α.sub.b =+/-π/4 (2) α.sub.a =0 and α.sub.b =+π/4 (3) α.sub.a =0 and α.sub.b =-π4 (4) where α a represents the angular difference between the principle polarization axes (φ0, φ1) of the linear polarizer and the associated quaterwave plate of one of the circular polarizers; and α b represents the angular difference between the principle polarization axes (φ2, φ3) of the linear polarizer and the associated quaterwave plate of the other circular polarizer, so that said four recorded conoscopic holograms have the following transfer functions respectively; Ta=1+cos .sup.α r.sup.2 ( 1) Tb=1-cos .sup.α r.sup.2 ( 2) Tc=1-sin2(Ψ-φ0)sin hu αr.sup.2 ( 3) Td=1+sin2(Ψ-φ0)sin .sup.α r.sup.2 ( 4) (ii) digitizing said four conoscopic holograms to form four digital signals each corresponding to one of said four conoscopic holograms, and (iii) combining the four digital signals by (a) linearly subtracting firstly the digital signal corresponding to Tb from the digital signal corresponding to Ta, and secondly the digital signal corresponding to Tc from the digital signal corresponding to Td to form the following transfer functions: T0=cos αr.sup.2 T1 (φ0)=sin(2(Ψ-φ0)sin αr.sup.2 which, putting φ0=0 and φ0 =π/4 reduce respectively to: T1(0)=sin[2/Ψ]sin αr.sup.2 T1(π/4)=cos2 Ψsin αr.sup.2 (b) determining the Fourrier transform T0 and T1 of the above-mentioned transfer functions T0 and T1; (c) performing the following linear combination T2=T0 30 j sin2θT1(0)+j cos2 θT1(π/4); and (d) subtracting jβ0/π from T2 if βρ 2 1, or subtracting j T 0/(β0ρ 2 ) from T2 for higher values of βρ 2 , in order to obtain the complex hologram, where: Ψ represents the slope relative to a reference plane including the optical axis of the system of a plane defined by the same optical axis and by the incident wave vector S; r.sup.2 =x'.sup.2 +y'.sup.2 where x', y' represents coordinates in the plane of the hologram; θ and ρ represents variable corresponding to T and r in the spectrum domain; β=π 2 /α; and β0 corresponds to the mean plane of the object.

Claim 19

A method of generating a quasi-complex hologram using incoherent light and a conoscopic system comprising a birefrigerant crystal inserted between two circular polarizers, the method comprising the following steps: (i) recording four conoscopic holograms of the same object without relative displacement thereof in the following respective different polarization configurations with circular polarizers constituted by respective linear polarizers and respective quaterwave plates capable of relative rotation: α.sub.a =α.sub.b =+/-π/4 (1) α.sub.a =-α.sub.b =+/-π/4 (2) α.sub.a =0 and α.sub.b =+π/4 (3) α.sub.a =0 and α.sub.b =-π4 (4) where α a represents the angular difference between the principle polarization axes (φ0, φ1) of the linear polarizer and the associated quaterwave plate of one of the circular polarizers; and α b represents the angular difference between the principle polarization axes (φ2, φ3) of the linear polarizer and the associated quaterwave plate of the other circular polarizer, so that said four recorded conoscopic holograms have the following transfer functions respectively; Ta=1+cos .sup.α r.sup.2 ( 1) Tb=1-cos .sup.α r.sup.2 ( 2) Tc=1-sin2(Ψ-φ0)sin hu αr.sup.2 ( 3) Td=1+sin2(Ψ-φ0)sin .sup.α r.sup.2 ( 4) (ii) digitizing said four conoscopic holograms to form four digital signals each corresponding to one of said four conoscopic holograms, and (iii) combining the four digital signals by (a) linearly subtracting firstly the digital signal corresponding to Tb from the digital signal corresponding to Ta, and secondly the digital signal corresponding to Tc from the digital signal corresponding to Td to form the following transfer functions: T0=cos αr.sup.2 T1 (φ0)=sin(2(Ψ-φ0)sin αr.sup.2 which, putting φ0=0 and φ0 =π/4 reduce respectively to: T1(0)=sin[2/Ψ]sin αr.sup.2 T1(π/4)=cos2 Ψsin αr.sup.2 (b) determining the Fourrier transform T0 and T1 of the above-mentioned transfer functions T0 and T1; (c) performing the following linear combination T2=T0 30 j sin2θT1(0)+j cos2 θT1(π/4); and (d) subtracting jβ0/π from T2 if βρ 2 1, or subtracting j T 0/(β0ρ 2 ) from T2 for higher values of βρ 2 , in order to obtain the complex hologram, where: Ψ represents the slope relative to a reference plane including the optical axis of the system of a plane defined by the same optical axis and by the incident wave vector S; r.sup.2 =x'.sup.2 +y'.sup.2 where x', y' represents coordinates in the plane of the hologram; θ and ρ represents variable corresponding to T and r in the spectrum domain; β=π 2 /α; and β0 corresponds to the mean plane of the object.