Optical transfer function an overview sciencedirect topics. For example, the transfer function of an electronic filter is the voltage amplitude at the output as a function of the frequency of a constant amplitude sine wave applied to the input. Pdf focal shift, optical transfer function, and phasespace. The optical transfer function of imaging optics is carried out with a plurality of tilted edges with respect to the edgeresponse detection line. In order to understand the significance of mtf, consider some general principles and practical examples for. Determination of the optical transfer function directly from. Over the past few decades new instruments, including the laser interferometer, the ccd. However, the latter part may often be omitted because image detectors generally are not phase sensitive. This work covers spatial frequency, spread function, wave aberration, and transfer function and how these concepts are related in an optical system, how they are. This reference work provides information on the optical transfer function. Point spread function psf image of a point source the transfer function of diffraction is the fourier transform of the psf called the optical transfer function otf diffractionlimited psf incoherent light, circular aperture where j 1 is the bessel function of the first kind and the normalized radius r is given by, psf r. This matlab function computes the inverse fast fourier transform of the optical transfer function otf and creates a pointspread function psf, centered at the origin. Focal shift, optical transfer function, and phasespace representations. Introduction to the optical transfer function spie digital library.
The tx and lo lasers are not phase locked with each other c. The rae equipmentfor measuring on is now organized in collaboration with. Diffraction at the system aperture self luminous points. The case of the defocused gaussian pupil is examined as a. The case of the defocused gaussian pupil is examined as a standard paradigm for understanding the otf in many imaging systems having that pupil. A formula for the mean human optical modulation transfer. We derive expressions for the transfer functions of double and multiplecavity fabryperot filters driven by laser sources with lorentzian spectrum. Shaw montana state university optical transfer function otf modulation transfer function mtf the optical transfer function otf is a complexvalued function describing the response of an imaging system as a function of spatial frequency. A mathematical proof for this method is presented with comparison to known degradation functions of linear motion. It covers basic linear systems theory and the relationship between impulse response, resolution, mtf, otf, ptf, and ctf. The optical image quality is influenced by aberrations, by diffraction, and by other factors, such as flare or stray light originating from the badly polished surfaces of lenses, from the edges of the mount, from striations and bubbles in the glass, and from unwanted double reflections. Diffraction, point spread function, psf with aberrations, optical transfer function. The modulation transfer function is the magnitude response of the optical system to sinusoids of different spatial frequencies.
Otf psf2otfpsf computes the fast fourier transform fft of the pointspread function psf array and creates the optical transfer function array, otf, that is not influenced by the psf offcentering. Temporal and spatial coherence spatially incoherent imaging the incoherent psf the optical transfer function otf and modulation transfer function mtf mtf and contrast comparison of spatially coherent and incoherent imaging next two weeks applications of the mtf. The schematic of a generic optical combiner an x junction waveguiding structure is used to combines the functions of the optical splitter and combiner. The range correction is given for extrapolating laser range measurements to the center of mass of the satellite. The optical transfer function is defined as the fourier transform of the impulseresponse of the optical system, also called the point spread function.
Introduction to the optical transfer function spie press. Convert pointspread function to optical transfer function. The image quality of an optical or electrooptical system can be characterized by either the systems impulse response or its fourier transform, the transfer function. In coherent optical systems, intradyne reception is employed. Dec, 2015 the optical transfer function is a complex transfer function where the modulus of the function describe the modulation transfer and the argument of the function describe the phase transfer in an. A formula for the mean human optical modulation transfer function as a function of pupil size andrew b.
The optical transfer function otf is a complexvalued function describing the response of an imaging system as a function of spatial frequency. Michael morris diffractive lenses differ from conventional optical elements in that they can produce more than one image. Pdf to text, how to convert a pdf to text adobe acrobat dc. A method for obtaining the optical transfer function from the edge spread function is described. The corresponding analysis, without the use of transfer functions, requires convolution of the corresponding impulse responses. Actually, in a course of fourier optics the students have the tools to be trained on the image formation theory, taking into account diffraction and the pupil function with wave aberration. Psf otf2psf otf, sz specifies the size, sz, of the output pointspread function. The optical transfer function is defined as the fourier transform of the impulse response of the optical system, also called the point spread function. It also defines important parameters that should be specified in connection with optical transfer function testing. Optical transfer function input ix,y electro optical system output image ux,y x y x y the otf describes resolution of an imagesystem.
Determination of the optical transfer function directly. Abstract, the working group on optical and modulation transfer. From the above we see the otf is the normalized fourier transform of the psf. Image formation and optical transfer function in a course.
The psf of an optical system is the irradiance distribution that results from a single point source in object space. Osa transfer functions of double and multiplecavity. Optical transfer function 149 the perfect otf 152 perfect otf from spread function 158 effects of certain aberrations on the optical transfer function 162 apodization 170 the geometrical optics otf approximation 177 the polychromatic otf 178 references 179 6. Tutorial solutions 4 optical transfer function range of problems associated with the otf. Recommendationsfor measurement of the optical transfer function of optical devices. Us7518712b2 tilted edge for opticaltransferfunction. For optical imaging devices, the optical transfer function is the fourier transform of the point spread function hence a function of spatial frequency. Optical transfer function analysis of single pinhole glasses. Optical design and image criteria 181 the nature of optical design 181. This tutorial introduces the theory and applications of mtf, used to specify the image quality achieved by an imaging system. Using ocr in adobe acrobat export pdf, document cloud, reader. Pdf we present a method for measuring the optical transfer function otf of a camera lens using a tartan test pattern containing sinusoidal functions. Finally, a system with a cubic phase mask is used as an example to illustrate the way to achieve the optical transfer function. Modulation transfer function in optical and electro.
Effects of diffraction efficiency on the modulation. Those concerned with grounding engineers and scientists in the procedures of optical evaluation have found that spatial frequency, wavefront distortion, and optical transfer function, though not particularly difficult concepts to understand, do not easily become part of ones thinking, and therefore practice, as the concepts of rays, ray tracing, and ray aberrations. Pixel level opticaltransferfunction design based on the. Chapter 32 handbook of optics photonics research group. The reasons for this and the consequences for an enhanced gamma curve are discussed. For most incoherent imaging systems, we are most interested in the magnitude of the otf, called the modulation transfer function mtf. With the growing role played by optical devices in measurement, communication, and photonics, there is a clear need for characterizing optical components.
Introduction to the optical transfer function book, 1989. For the otf to become a part of our everyday thinking, we need to understand the full meaning and the essence of certain basic concepts. It is used by optical engineers to describe how the optics project light from the object or scene onto a photographic film. The onorbit identification of the transfer function tf of a spaceborne optical telescope is useful for the acceptance test of the instrument, for the onorbit refocusing and. These are of interest because of their applications in sensing and channel filtering in optical frequencydivision multiplexing networks. A basic and useful parameter, especially for imaging systems, is the modulation transfer function, or mtf. Temporal and spatial coherence spatially incoherent imaging the incoherent psf the optical transfer function otf and modulation transfer function mtf mtf and contrast comparison of spatially coherent and incoherent imaging next two weeks applications of the mtf diffractive optics and holography. Pdf measurement of the lens optical transfer function using a. Since optical objects are complex entities, the complete transfer function of the microscope, called optical transfer function otf, consists of the ctf together with a phase transfer function. Introduction to the optical transfer function 2002. Originally published by wiley in 1989, this timeless classic provides a wellillustrated treatment of the fundamental concepts of spatial frequency, spread function, wave aberration, and transfer function and how these concepts are related in an optical system, how they are measured and calculated, and how they may be useful. The optical transfer function is thus readily obtained by first acquiring the image of a point source, and applying the twodimensional discrete fourier transform to the sampled. The optical transfer function and the meijerg function.
This section is an index to our various discussions, references, and interactive java tutorials on the modulation transfer function. The resolution and performance of an optical microscope can be characterized by a quantity known as the modulation transfer function mtf, which is a measurement of the microscopes ability to transfer contrast from the specimen to the intermediate image plane at a specific resolution. Psf otf2psfotf computes the inverse fast fourier transform of the optical transfer function otf and creates a pointspread function psf, centered at the origin. The optical transfer function otf of an optical system such as a camera, microscope, human eye, or projector specifies how different spatial frequencies are handled by the system. Optical transfer function analysis of circularpupil. The measurement of the optical transfer functions of.
Pixel level opticaltransferfunction design based on the surfacewaveinterferometry aperture guoan zheng,1, yingmin wang,2 and changhuei yang1,2 1department of electrical engineering. Otf modulation transfer function mtf montana state university. More importantly, the topic of this book is not subject to obsolescence like computer memory is to moores law. With optical character recognition ocr, acrobat works as a text converter, automatically extracting text from any scanned paper document or image and converting it to a pdf. It parallels the concept of electrical transfer function, about transformation of an object ix,y to its image ux,y. Hitherto this has been only loosely specified in itur bt. The modulation transfer function of a lens, microscope objective, or other optical system is a measurement of its ability to transfer contrast at a particular resolution level from the object or specimen to the image. Hold it so close that is it completely out of focus, then squint. Optical transfer function otf modulation transfer function mtf the optical transfer function otf is a complexvalued function describing the response of an imaging system as a function. Transfer functions are a powerful tool for analyzing optical and electrooptical.
When optical designers attempt to compare the performance of optical systems, a commonly used measure is the modulation transfer function mtf. The gain function and active reflecting area of the array have been computed for estimating. A telescope forming an image of a distant star is a good example. The profile of the optical transfer function for the best focus plane is within the dotted lines. Modulation transfer function mtf the most commonly used diffractionbased image quality metrics are point spread function psf encircled or. Mtf is used for components as simple as a spherical singlet lens to those as complex as a multielement telecentric imaging lens assembly. This standard specifies an eotf characterizing highdynamicrange reference displays used primarily for mastering nonbroadcast content. Signals are now the spatial distributions of the radiant power density in. In order to understand the significance of mtf, consider some. Review of basic principles in optics, wavefront and. Another important concept is the optical transfer function otf, which represents the ratio of image contrast to specimen contrast when plotted as a function of spatial frequency, taking into account the phase shift between positions occupied by the actual and ideal image. Adobe acrobat export pdf supports optical character recognition, or ocr, when you convert a pdf file to word.
Functions is concerned with otf and mtf standards, with compara tive lens testing using. Any serious student interested in a career in the semiconductor industry or lithography should consider this book as a must read. The onorbit identification of the transfer function tf of a spaceborne optical telescope is useful for the acceptance test of the instrument, for the onorbit refocusing and for the restoration of the recorded images. That is, h u, v f h x, y, where u, v are the spatialfrequency coordinates at the focal plane. The method involves the inversion of a fredholm integral equation of the first kind using samplingtheory concepts. Optical design with zemax phd basics 5 aberrations ii. It refers to a mathematical technique of analysing and designing optical systems. Quality criteria, like strehi ratio, resolving power and. Abstract the meijerg functions are applied in the calculation of the optical transfer function otf for systems with circular pupil.
An optical transfer function has been computed for the retroreflector array carried by the starlette satellite 1975 10a. Introduction to modulation transfer function edmund optics. Effects of diffraction efficiency on the modulation transfer function of diffractive lenses dale a. Chapters 8 and 9 and notes derived from a highly recommended book by chris mack, fundamental principles of optical lithography. Demonstration role of pupil size and defocus on retinal blur draw a cross like this one on a page. Image resolution limits resulting from mechanical vibrations. Introduction to the optical transfer function charles. Pdf optical transfer function identification from satellite. The modulus of the otf is called the modulation transfer function, mtf. These effects are harmful, but they cannot always be avoided. Fundamental concepts of spatial frequency, spread function, wave aberration and transfer function are related to optical systems, with discussions of their measurements, calculations and uses.
The spread function of the image motion is the probability density function pdf or the histogram of the image motion during the exposure time. Convert optical transfer function to pointspread function. Pdf abstract the meijerg functions are applied in the calculation of the optical transfer function otf for systems with circular pupil. By using the otf, you can often decompose the description of an optical system into the equivalent of a product of transfer functions. The resolution criteria based on fourier optics are. Typical examples for both symmetric and asymmetric edge spread functions are studied and compared with the known solutions. After a short survey of the theoretical relations between the optical transfer function and the image aberrations and diffraction, the basic requirements for the. The effect of the tilt is to stretch out the edge response so that fine details can be detected even operating at a spatial frequency below the nyquist limit of the detector. Optical transfer function otf modulation transfer function. Pdf the optical transfer function and the meijerg function. When we analyze an optical system in the frequency domain, we consider the imaging of sinewave inputs fig. For example, when several optical subsystems are combined, the overall transfer function is the multiplication of the individual transfer functions.
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