(光学系统像质评价).doc

Chapter X Image quality evaluation of optical system (光学系统像质评价)Introduction10.1 Brightness of center disk and Rayleigh Judgement (中心点亮度和瑞利判断)10.2 Resolving power (分辨率)10.3 Spot diagram (点列图)10.4 Optical transfer function (光学传递函数)Introduction The initial preliminary evaluation of the image quality provided by a particular system come from the blur circle formed by all the rays emitted by point objects in different field of view. This blur circle is called usually as diffused disk, spot diagram, point spread function.1. Geometrical aberration: The geometrical aberration is the residual aberration less than the tolerance of aberration or according to the curve of aberration. We determine the dimension of diffused disk. Because of diffraction geometrical aberration can not describe the actual distribution of energy of a point object.2. Wavefront aberration Rayleigh criterion (if the image quality is good; ifthe image quality is perfect) is very simple, it is does not consider the defect area. Only used in small aberration system. (Peak to Valley: maximum wavefront aberration) 3. The resolving power of an optical system has been the criterion most used for the quality of the image. It has been expressed by in terms of the maximum number of lines per millimeter. Moreover, the resolving power depends greatly on the contrast in object.4. Optical Transfer Function (OTF) OTF represents the property of an optical system considered as a transmitter of spatial frequence. Even an ideally corrected system can only transmit spatial frequence below some limiting frequence-cutoff frequence.10.1 Brightness of center disk and Rayleigh Judgement (中心点亮度和瑞利判断)1. Brightness of center diskStrehl Criterion: Let Get Expansion series of Sample: It corresponds to the Rayleigh criterion. 2. Rayleigh Judgement The image quality is good The image quality is perfect Considering only the maximum wavefront aberration, defocusing can improve the wavefront aberration. (Select the best image plane) The ration of the area () to the whole area is not considered. The advantage is easy to calculate, applied in optical system with small aberration, such as telescope, microscope objective.Zemax: analysis wavefront window Opd: determine the defect area 10.2 Resolving power (分辨率) Resolving power of a system will be of the order of , is the mean circle diameter of diffused disk. Rayleigh Judgement: the least resolving separation (LRS) of the two star images is given by the radius of Airy Disk. LRS=1 Airy radius Dove Judgement: LRS=0.85 Airy radius Ideal optical system: Telescope Microscope Photographic Resolving power depend on Applied in large aberration system, such as photographic lens.Discussion: Resolving plate is a square-wave grating which consists of a series of light and darkness at progressively closer spacing.The resolving plate is high contrast, while object is lower contrast. Some times it appears pseudo-resolving phenomenon, below cutoff frequence, higher frequence object can be resolved, this is because of phase-inverted.10.3 Spot diagram (点列图) The entrance pupil is divided into a few equal area rings, equal number of rays pass through each zone. The points distribution in image plane represents the energy distribution. The diameter of the spot less than (0.030.01mm) is permitted, and it is depended on the detector.10.4 Optical transfer function (光学传递函数)The base of OTF is Fourier analysis1. Concept An incoherent optical system (incoherent illumination) can be considered as a low-pass linear filter of spatial frequencies. If sinusoidal intensity distribution (signal) is inputted into optical system, the output is also sinusoidal, but the contrast is reduced (K1), phase is shifted ().The ration M1/M and phase are depends on the frequence. M: inputted object contrast M1: outputted image contrast The ratio M1/M is called modulated transfer function (MTF) of an optical system, and is called phase transfer function (PTF).Inputted: After passing though optical system Why take fine-wave distribution signal as inputted object? Because any object can be seen as be composed by a series of sine patterns with different frequence and different brightness.2. The condition of OTF1) linear condition: Energy distributions of object (image) satisfy linear superposition:l with incoherent illuminationl ground glassl optical system has larger numerical aperture2) space-invariableThere is the same point spread function (PSF) in any region of the image plane-isoplanatic condition. Object (image) is divided into many isoplanatic regions, each region has the same effect of diffraction and aberration.3. Expression of OTFIn order to calculate OTF the object (image) break down many points, mathematically is.Object distribution: Image distribution: h PSF (point spread function) Method 1: Method 2: Fourier transformMethod 1: measured by interferometer;Method 2: measured by MTF instrument.Sample: Using linear spread function (LSF) LSF: Similarly: Fourier transform OTF：, () MTF: PTF: Linear spread function (LSF) can be analogized by scanning slit.4. Example Let Image distribution Suppose: Result:5. Application of OTF Analysis Limiting frequence: curve better than . Low frequence: curve better than . It means that lens has better image quality for low frequence object than lens. Integrate the curve, the larger the area is, the better the lens quality is. The area represents the transmitted information magnitude. The advantage of using MTF as quality criterion is the ability to cascade the MTF curves of a lens and film by multiplying together the MTF values. Notes that: If the illumination is perfectly coherent, the resolution drops to half, but the contrast at the low frequence is great improved.6. The calculation of exit pupil function OTF is the autocorrelation of exit pupil function R Distance from ideal point to center of exit pupil. C Constant, used for normalized OTF. Constant (amplititude), can be discarded. wavefront aberration. Tangential: Sagittal: 附一 Normally For geometrical optics, assume that tends towards zero, so we can write: 这里的坐标即像差中出瞳。附二OptikosS