Nonlinear Fuzzy PID Control Phase plane analysis Standard surfaces Performance.
Phase Control: Nonlinear Phase Constrast
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Nonlinear Phase Constrast Carlos Gerardo Treviño-Palacios, Marcelo David Iturbe-Castillo, David Sánchez-de-la-Llave, Ruben Ramos-García and Luis Ignacio Olivos-Pérez T he refractive index of many optical materials depends on the intensity of the light propagating through the mate- rial. Processes that occur as a result of the nonlinear refractive index (NLRI) are phase conjugation, self-focusing, optical bistability, two beam coupling and opti- cal solitons. The NLRI can also be used to photoinduce phase filters in image for- mation systems. Phase filters are needed to implement the phase constrast tech- nique used to contrast phase objects. Phase objects are traditionally contrasted by using phase-contrast or interferomet- ric techniques to convert phase changes into amplitude changes and to visualize them. 1,2 Recently we reported a single lens optical image processor using a non- linear medium which has the robustness of phase contrast methods based on a NLRI medium. 3 Figure 1(a) illustrates the single lens image processor. The object under test is uniformly illuminated and a thin positive lens is used to obtain both the phase object’s Fourier transform and its image. An intensity-dependent medium (IDM) is placed at the system’s focal plane and the intensity distribution is observed at the image plane of the sys- tem. On the focal plane of the lens, the field distribution consists of a zero fre- quency at the center and additional fre- quencies surrounding it. At this plane, the IDM produces a self-aligned pho- toinduced phase filter which follows the intensity of the Fourier spectrum. Since the aim is to realize phase contrast with- out distorting the image, it is desirable that the photoinduced filter alter only a small area around the zero frequency. To attain adequate filtering, a total illu- mination area larger than the phase object area must be employed while the intensity of the illuminating wave front is controlled. We can describe this setup from two different viewpoints. From an image processing point of view, if only the object is illuminated, the photoinduced 30 Optics & Photonics News ■ December 2003 PHASE CONTROL filter follows the object intensity spec- trum and in general the resulting image intensity cannot be used to recover the object phase distribution. When there is illumination beyond the geometrical boundaries of the object, more energy is tightly concentrated near the zero fre- quency. This energy is responsible for photoinducing an adequate filter on the IDM. From an interferometric point of view, we can conceptually divide in two the total Fourier spectrum at the focal plane as the zero frequency region and the additional information surrounding it. The illumination beyond the phase object area will concentrate around the zero frequency, while the object spec- trum energy is distributed along larger frequency components. If a sufficiently large illumination area is used, an ade- quate phase difference will exist between the zero frequency region and the rest of the spectrum, allowing interference with good contrast. The simple and robust single lens setup described is used to visualize phase distributions, from the aberra- tions in a lens [Fig. 1(b)] to an air flow [Fig. 1(c)]. The required filtering can be Figure 1. (a) Single lens nonlinear common path interferometer setup. f is the focal length of the lens, d o and d i are the object and image distances of the setup lens, respectively. IDM is an intensity dependent medium, (b) contrasted image of reading glasses and (c) contrasted image of the temperature distribution induced in air by a lit lighter using a bleached photo- graphic film as IDM. optically self-induced in different nonlinear optical materials. The phase object distribution can be recovered using the phase retrieval techniques used in interferometry. We foresee applications including visualization and analysis of a variety of phase objects and the illustration of optics principles in K-12 level classrooms. References 1. J.W. Goodman, Introduction to Fourier Optics (McGraw Hill, San Francisco, 1968). 2. D. Malacara, Optical Shop Testing (John Wiley & Sons, New York, 1991). 3. C.G. Treviño-Palacios, M. D. Iturbe-Castillo, D. Sánchez-de-la-Llave, R. Ramos-García and L. I. Olivos- Pérez, “Nonlinear common-path interferometer: an image processor,” Appl. Opt. 42, 25 (2003). In press. Carlos Gerardo Treviño-Palacios (carlost@inaoep. mx), Marcelo David Iturbe-Castillo, David Sánchez- de-la-Llave, Ruben Ramos-García and Luis Ignacio Olivos-Pérez are with the Instituto Nacional de Astrofísica, Optica y Electrónica Puebla, México. (a) Object Lens IDM Image plane d o d i f (b) (c) Tell us what you think: http://www.osa-opn.org/survey.cfm
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Transcript of Phase Control: Nonlinear Phase Constrast
Nonlinear Phase ConstrastCarlos Gerardo Treviño-Palacios, Marcelo David Iturbe-Castillo, David Sánchez-de-la-Llave, Ruben Ramos-García and Luis Ignacio Olivos-Pérez
The refractive index of many opticalmaterials depends on the intensity of
the light propagating through the mate-rial. Processes that occur as a result of thenonlinear refractive index (NLRI) arephase conjugation, self-focusing, opticalbistability, two beam coupling and opti-cal solitons. The NLRI can also be used tophotoinduce phase filters in image for-mation systems. Phase filters are neededto implement the phase constrast tech-nique used to contrast phase objects.Phase objects are traditionally contrastedby using phase-contrast or interferomet-ric techniques to convert phase changesinto amplitude changes and to visualizethem.1,2 Recently we reported a singlelens optical image processor using a non-linear medium which has the robustnessof phase contrast methods based on aNLRI medium.3
Figure 1(a) illustrates the single lensimage processor. The object under testis uniformly illuminated and a thinpositive lens is used to obtain both the phase object’s Fourier transform and itsimage. An intensity-dependent medium(IDM) is placed at the system’s focalplane and the intensity distribution isobserved at the image plane of the sys-tem. On the focal plane of the lens, thefield distribution consists of a zero fre-quency at the center and additional fre-quencies surrounding it. At this plane,the IDM produces a self-aligned pho-toinduced phase filter which follows theintensity of the Fourier spectrum. Sincethe aim is to realize phase contrast with-out distorting the image, it is desirablethat the photoinduced filter alter only asmall area around the zero frequency.To attain adequate filtering, a total illu-mination area larger than the phaseobject area must be employed while theintensity of the illuminating wave frontis controlled.
We can describe this setup from twodifferent viewpoints. From an imageprocessing point of view, if only theobject is illuminated, the photoinduced
30 Optics & Photonics News ■ December 2003
PHASE CONTROL
filter follows the object intensity spec-trum and in general the resulting imageintensity cannot be used to recover theobject phase distribution. When there isillumination beyond the geometricalboundaries of the object, more energy istightly concentrated near the zero fre-quency. This energy is responsible forphotoinducing an adequate filter on theIDM. From an interferometric point ofview, we can conceptually divide in twothe total Fourier spectrum at the focalplane as the zero frequency region andthe additional information surroundingit. The illumination beyond the phaseobject area will concentrate around thezero frequency, while the object spec-trum energy is distributed along largerfrequency components. If a sufficientlylarge illumination area is used, an ade-quate phase difference will exist betweenthe zero frequency region and the rest ofthe spectrum, allowing interference withgood contrast.
The simple and robust single lenssetup described is used to visualizephase distributions, from the aberra-tions in a lens [Fig. 1(b)] to an air flow[Fig. 1(c)]. The required filtering can be
Figure 1. (a) Single lens nonlinear common path interferometer setup. f is the focal length ofthe lens, do and di are the object and image distances of the setup lens, respectively. IDM is anintensity dependent medium, (b) contrasted image of reading glasses and (c) contrastedimage of the temperature distribution induced in air by a lit lighter using a bleached photo-graphic film as IDM.
optically self-induced in different nonlinear optical materials. The phaseobject distribution can be recoveredusing the phase retrieval techniquesused in interferometry. We foresee applications including visualization andanalysis of a variety of phase objects andthe illustration of optics principles in K-12 level classrooms.
References
1. J.W. Goodman, Introduction to Fourier Optics (McGrawHill, San Francisco, 1968).
2. D. Malacara, Optical Shop Testing (John Wiley & Sons,New York, 1991).
3. C.G. Treviño-Palacios, M. D. Iturbe-Castillo, D.Sánchez-de-la-Llave, R. Ramos-García and L. I. Olivos-Pérez, “Nonlinear common-path interferometer: animage processor,” Appl. Opt. 42, 25 (2003). In press.
Carlos Gerardo Treviño-Palacios ([email protected]), Marcelo David Iturbe-Castillo, David Sánchez-de-la-Llave, Ruben Ramos-García and Luis IgnacioOlivos-Pérez are with the Instituto Nacional deAstrofísica, Optica y Electrónica Puebla, México.
(a)Object Lens IDM Image plane
do di
f
(b) (c)
Tell us what you think: http://www.osa-opn.org/survey.cfm
