如何测量调制传递函数How to Measure Modulation Transfer Function
How to Measure Modulation Transfer Function
https://www.360docs.net/doc/b616864637.html,/blog/?p=1294
How to Measure Modulation Transfer Function (1)
In a simple wording, the modulation transfer function or MTF is a measure of the spatial resolution of an imaging component. The latter can be an image sensor, a lens, a mirror or the complete camera. In technical terms, the MTF is the magnitude of the optical transfer function, being the Fourier transform of the response to a point illumination.
The MTF is not really the most easiest measurement that can be done on an imaging system. Various methods can be used to characterize the MTF, such as the “slit image”, the “knife edge”, the “laser-speckle technique” and “imag ing of sine-wave patterns”.It should be noted that all method listed, except the “laser-speckle technique, measure the MTF of the complete imaging system : all parts of the imaging system are included, such as lens, filters (if any present), cover glass and image sensor. Even the effect of the processing of the sensor’s signal can have an influence on the MTF, and will be include in the measurement.
In this first MTF-blog the measurement of the modulation transfer function based on imaging with a sine-wave pattern will be discussed. It should be noted that in this case dedicated testcharts are used to measure the MTF, but the pattern on the chart should sinusoidally change between dark parts and light parts. In the case a square-wave pattern is used, not the MTF but the CTF (= Contrast Transfer Function) will be measured. And the values obtained for the CTF will be larger than the ones obtained for the MTF.
The method described here is based on the work of Anke Neumann, written down in her MSc thesis “Verfahren zur Aufloesungsmessung digitaler Kameras”, June 2003.The basic idea is to use a single testchart with a co-called Siemens-star. An example of such a testchart is illustrated in Figure 1.
Figure 1 : Output image of the camera-under-test observing the Siemens star.
(Without going further into detail, the testchart contains more structures than used in the reported measurement performed for the MTF.) The heart of the testchart is the Siemens star with 72 “spokes”.As can be seen the distance between the black and white structures on the chart is becoming larger if one moves away from the center of the chart. In other words, the spatial frequency of the sinusoidal pattern is becoming lower at the outside of the Siemens star, and is becoming higher closer to the center of the Siemens star. Around the center of the Siemens star, the spatial frequency of the sinusoidal pattern is even too high to be resolved by the camera-under-test and aliasing shows up. In the center of the Siemens star a small circle is included with 2 white and two black quarters. These are going to play a very important role in the measurements.
The measurement procedure goes as follows :
1.Focus the image of the Siemens star, placed in front of the camera, as good as possible
on the imager. Try to bring the Siemens star as close as possible to the edges (top and bottom) of the imager,
2.Shoot an image of the testchart (in the example described here, 50 images were taken
and averaged to limit the temporal noise).
In principle, these two steps is all one needs to be able to measure/calculate the MTF. But to obtain a higher accuracy of the measurements, the following additional steps might be required :
1.Cameras can operate with or without a particular offset corrected/added to the output
signal. For that reason it might be wise to take a dark reference frame to measure the offset and dark signal (including its non-uniformities) for later correction. In the experiments discussed here, 50 dark frames were taken and averaged to minimize the temporal noise.
2.The data used in the measurement is coming from a relatively large area of the sensor
and is relying on an uniform illumination of the complete Siemens star. Moreover, the
camera is using a lens and one has to take into account the lens vignetting or intensity fall-off towards the corners of the sensor. For that reason a flat-fielding operation might be needed : take an image of a uniform test target, and use the data obtained to create a pixel gain map. In the experiments discussed her, 50 flat field images were taken and averaged to minimize the temporal noise.
3.The camera under test in this discussion delivers RAW data, without any processing. If
that was not the case it would have been worthwhile to check the linearity of the camera
(e.g. use of a gamma correction) by means of the grey squares present on the testchart
as well.
Taken all together the total measurement sequence of the MTF characterization is then composed of :
1.Shoot 50 images of the focused testchart, and calculate the average. The result is
called : Image_MTF,
2.Shoot 50 flat field images with the same illumination as used to shoot the images of the
focused testchart, and calculate the average image of all flat field images. The result is called :Image _light,
3.Shoot 50 images in dark, and calculate the average image of all dark image. The result is
called Image_dark,
4.Both Image_MTF and Image_light are corrected for their offset and dark
non-uniformities by subtracting Image_dark,
5.The obtained correction (Image_light–Image_dark) will be used to create a gain map
for each pixel, called Image_gain,
6.The obtained correction (Image_MTF – Image_dark) will be corrected again for any
non-uniformities in pixel illumination, based on Image_gain.
If this sequence is followed, an image like the one shown in Figure 1 can be obtained.
1.Next the pixel coordinates of the center of the testchart need to be found. This can be
done manually or automatically. The latter is done in this work, based on the presence of the 4 quadrants in the center of the testchart.
2.Once the centroid of the testchart is known, several concentric circles are drawn with
the centroid of the testchart as their common center. An example of these concentric circles on top of the testchart is shown in Figure 2.
Figure 2 : Siemens star with concentric circles (shown in green), with their centers coincides with the centroid of the testchart (red cross).
1.After creating the circles, the sensor output values of the various pixels lying on these
circles are checked. On every circle the pixel values change according to a sine wave, of which the frequency is known (72 complete cycles of the sine wave and it radius, in number of pixels, can be calculated). For each of the circles, a theoretical sine wave can be fitted through the measured data. Consequently for each circle a parameter can be found that corresponds to the amplitude of the fitted sine wave.
2.In principle the MTF curve could be constructed, the only missing link is the value of the
MTF for very low frequencies close to DC. This value can be found as the difference between the white values and black values of the four quadrants right in the middle of the testchart.
3.Normalizing the obtained data completes the MTF curve : the calculated amplitudes of
the sine waves are normalized with the signals of the four quadrants in the middle of the chart, the frequencies of the sine waves are normalized to the sampling frequency of the imager (6 mm pixel pitch).
The outcome of the complete exercise is shown in Figure 3.
Figure 3 : Modulation Transfer Function of the camera-under-test.
As indicated in Figure 3, the MTF measurement is done with white light created by 3 colour LED arrays (wavelengths 470 nm, 525 nm, 630 nm). As can be seen from the curve, the camera has a relative low MTF, around 8 % at Nyquist frequency (f N). In theory an imager with a large fill factor can have an MTF value of 60 % at f N. But this camera is performing far away from this theoretical value. But one should not forget, this MTF measurement does include ALL components in the imaging system, not just the sensor !
Now that the MTF measurement method is explained, in the next blogs more MTF results will be shown and compared.
Albert, 20-02-2014.
How to Measure Modulation Transfer Function (2)
In the previous blog, the measurement of the Modulation Transfer Function by means of the Siemens star was explained. In this blog, this method will be applied to check out the effect of the lens F-number on the MTF.
In Figure 1 the result of the MTF measurement is shown.
Figure 1 : Modulation Transfer Function for two settings of the lens F-number.
It is quite nice to see the influence of the F-number :
a low F-number is referring to a large lens opening (= a lot of light goes to the sensor, a
short exposure time is needed), and in that case the incoming light is reaching the sensor with a large chief-ray angle (= deviation from the normal),
? a large F-number is referring to a small lens opening (= much less light goes to the sensor,
a long exposure time is needed), and in that case the incoming light is reaching the
sensor with a small chief-ray angle (= almost perpendicular to the sensor).
Light that is perpendicularly reaching the sensor will suffer less from optical cross-talk in comparison to light that is reaching the sensor under a certain angle and is deviating more from the normal. More (optical) cross-talk does result in less contrast between neighbouring pixels, thus lowering the MTF for larger spatial frequencies. And this effect is observed in Figure 1 ! Next time something about colour and MTF.
Albert, 25-03-2014.
How to Measure Modulation Transfer Function (3)
A new measurement result in the MTF-series is shown in this blog : the MTF of a monochrome sensor, but no longer with white light input, but with red, green and blue light. Some interesting observations can be reported.
In Figure 1, the results of the MTF measurement are shown.
Figure 1 : Modulation Transfer Function of a monochrome device for various wavelengths of the incoming light.
It is quite nice to see the influence of the wavelength of the incoming light :
?The absorption coefficient of silicon for “red” photons, or photons with a l ower energy, is relatively low. The absorption depth for light with a wavelength of 630 nm can reach a few microns. So part of the electrons generated in the silicon will be generated below the depletion region of the photodiodes, and before these electrons can get collected by the photodiodes, they need to “travel” in the neutral bulk/epi-layer. Because there is no electrical field present in these regions to guide the electrons to the right photodiodes, the chance that these electrons finally land in a neighbouring pixel is relatively large. In this way the contrast in the image is reduced, so is the MTF,
?The absorption coefficient of silicon for “blue” photons, or photons with a higher energy, is relatively large. The absorption depth for light with a wavelength of 470 nm is just a few tens of a micron. So most of the electrons generated in the silicon will be generated within the depletion region and the chance of diffusion of these electrons to neighbouring pixels is limited. The contrast in the image is not reduced by the effect described above for the “red” photons, neither is the MTF,
?The green light, with a wavelength of 525 nm, has an absorption coefficient situated
between the red light and the blue light. So not surprising that the MTF for the green light is lying between the blue and red results.
The effect explained here by means of the MTF measurements is also known as electrical cross-talk. The loss in contrast or loss in MTF is due to the diffusion of electrons. The effect is also illustrated in Figure 2.
Figure 2 : Illustration of the electrical cross-talk.
Figure 2 shows a cross section of a hypothetical image sensor with an RGB filter. Illustrated is the fact that the “red” photons can penetrated much deeper into the silicon than the “blue” ones. This is the origin of the larger electrical cross-talk for the light having a longer wavelength. To conclude a few numbers :
?Absorption coefficient for a “red” photon (630 nm) = 4000/cm, resulting in an absorption depth of 2.5 um,
?Absorp tion coefficient for a “green” photon (525 nm) = 10,000/cm, resulting in an absorption depth of 1 um,
?Absorption coefficient for a “blue” photon (470 nm) = 20,000/cm, resulting in an absorption depth of 0.5 um.
Albert, 19-04-2014.
How to Measure Modulation Transfer Function (4)
The MTF or Modulation Transfer Function can be measured in various ways. In the previous MTF-blogs the measurement by means of a Siemens Star testchart was discussed. This method has particular advantages, but also has some limitations, mentioned in earlier blogs. Another evaluation technique to characterize the MTF is based on the so-called slanted-edge method. Explained in words, this method sounds very complicated, but in reality it is really pretty simple.
There are several good references describing the slanted-edge method, e.g. :
?M. Estribeau and P. Magnan., in SPIE Proceedings, Vol. 5251, Sept. 2003,
?T. Dutton et al. in SPIE Proceedings, Vol. 4486, 2002, pp. 219-246,
?P.B. Burns, in Proceedings IS&T, 2000, pp 135-138,
?S.E. Reichenback et al. In Optical Engineering, pp. 170-177, 1991.
This slanted edge method became an ISO standard, namely ISO 12233. This is one of the very few ISO standards for image sensor and/or camera measurements.
The technique of the slanted edge can be described as follows :
1.Image a vertically oriented edge (or a horizontal one for the MTF measurement in the
other direction) onto the detector. The vertical edge needs to be slightly tilted with
respect to the columns of the sensor. The exact tilting is of no importance, it is advisable to have a tilt of minimum 2o and maximum 10o w.r.t. the column direction. A tilt within these limits gives the best and most reliable results for the MTF characterization.
2.Each row of the detector gives a different Edge Spread Function (ESF), and the Spatial
Frequency Response (SFR) of the slanted edge can be “created” by checking the pixel values in one particular column that is crossing the imaged slanted edge.
3.Based on the obtained SFR, the Line Spread Function (LSF) can be calculated, the LSF is
simply the first derivative of the SFR.
4.Next and final step is calculating the Fourier transform of the LSF. This results in the
Modulation Transfer Function, because the MTF is equal to the magnitude of the optical transfer function, being the Fourier transform of the LSF. Plotting the MTF as a function of the spatial frequency can be done after normalizing the MTF to its DC component and normalizing the spatial frequency to the sampling frequency.
(In one of the coming blogs more info will be given on further improvement and/or sophistication of this procedure.)
A very helpful strategy in understanding how this MTF measurement method works and to check the algorithms, is to run a simulation and create an artificial image with a slanted edge that is sampled by an artificial sensor (e.g. with a pixel fillfactor of 100%). Next the theoretical, geometric MTF can be calculated as a sinc-function of the spatial frequency, while the synthetic image can be used as the input image to evaluate the MTF by means of the technique explained above (ESF, SFR, LSF, MTF). Such a simple simulation tool can also be used to check the influence of the various system parameters on the measurement technique. An example of such a simulation is shown in the following figures.
First of all a synthetic image is generated that results in a slanted edged of 4 deg. w.r.t. the column direction. A region-of-interest (ROI) of 200 (H) x 300 (V) pixels is created around the black-white transition of the slanted edge. This synthetic image is shown in Figure 1.
Figure 1 : ROI containing the slanted edge or black-white transition.
A particular column is selected (in this example column number 96), and all pixel values in this column are recorded to generate the SFR or Spatial Frequency Response. The result of this operation is shown in Figure 2, with reference to the left vertical axis.
Figure 2 : Spatial Frequency Response, being
the values of the pixels present in column 96 of the image shown in Figure 1, and Line Spread Function, being the first derivative of the SFR.
Next the LSF or Line Spread Function is generated, simply by numerically calculating the first derivative of the SFR. The LSF is shown in Figure 2 as well, with reference to the right vertical axis.
Once the LSF is known, the magnitude of the FFT of this LSF is calculated. Plotting the FFT magnitude versus spatial frequency results in the MTF of the sensor, as shown in Figure 3. Notice that the MTF is normalized with its value a zero input frequency (= DC), while the spatial frequency is normalized to the spatial sampling frequency of the sensor. In this simulation example, the pixel pitch is equal to 6.5 μm.
Figure 3 : MTF of the simulated pixel (6.5 μm, 100 % FF), as well as the theoretical, geometric MTF of the same pixel.
In Figure 3 and next to the outcome of the MTF simulation, also the theoretical geometric MTF of the pixel is shown (6.5 μm, 100 % FF), for comparison reasons. This geometrical MTF is calculated by means of the well-known sinc-function. As can be seen, both curves coincide very nicely, indicating that the slanted edge method and the algorithms used in the calculation seem to do the job that they were developed for !
Before showing real measurements, in the next blog(s) a few additional improvements of the slanted edge method will be highlighted.
Albert, 18-06-2014.
How to Measure Modulation Transfer Function (5)
In the last blog the MTF measurement based on the slanted edge was introduced. As mentioned
in that blog, to understand all ins and outs of the method, it is very beneficial to develop a small, simple model of the sensor with a slanted edge projected on it. And next, analyze the obtained, synthesized image. This simulation tool is also used here to check out the sensitivity of the technique w.r.t. the angle of the slanted edge.
The result is shown in Figure 1.
Figure 1 : Effect of the slanted edge angle on the accuracy of the evaluation technique to characterize the MTF.
Shown are the MTF results obtained for a simulation of the angle being equal to 2 deg., 4 deg., 6 deg., 8 deg., 10 deg. and 12 deg. The ideal curve, obtained by the calculation of the sinc-function, is included as well. As can be seen from the curve :
?All evaluations based on an angle between 2 deg. and 10 deg. seem to fit very well to the ideal curve,
?The simulation result for an angle of 12 deg. shows some minor deviations from the ideal curve.
As a message from this simulation : angles of the slanted edge between 2 deg. and 10 deg. are very well suited for the MTF analysis. Once the angle is larger than 10 deg., the slanted edge method starts loosing its accuracy. The simulation results obtained here are fully in line with the advice of the ISO standard, which suggests also to use an angle of the slanted edge between 2 deg. and 10 deg.
Next time : how to implement oversampling and how to avoid aliasing effects during the measurements.
Albert, 04-07-2014.
How to Measure Modulation Transfer Function (6)
Previous time it was explained that larger angles of the slanting edge may result in deviating MTF values. The results already presented in the previous post is repeated here in Figure 1.
Figure 1 : Effect of the slanted edge angle on the accuracy of the evaluation technique to characterize the MTF.
As a message from the simulation results shown in Figure 1 : angles of the slanted edge between 2 deg. and 10 deg. are very well suited for the MTF analysis. This can be seen by checking their comparison to the ideal curve (see black dots in Figure 1). Once the angle is larger than 10 deg., the slanted edge method starts loosing accuracy. The simulation results obtained here are fully in line with the advices of the ISO standard, which suggests also to use an angle of the slanted edge between 2 deg. and 10 deg. Just to highlight the deviations, an extra insert is included in Figure 1 to shown the MTF behaviour around the Nyquist frequency.
One of the reasons why angles larger than 10 deg. give deviating results is the fact that the number of measurement points in a particular sensor column is getting smaller and smaller if the angle is getting larger. This can indeed result in nasty effects on the MTF values and can lead to aliasing effects in the sampling of the data. To avoid these type of issues, it is possible to take the data of multiple columns into account instead of using the data of just a single column. To show the overall working principle of oversampling, the spatial frequency responses (SFR) of 4 neighbouring columns are shown before (Figure 2) and after (Figure 3) multiplexing the data into a single SFR.
Figure 2 : Spatial Frequency Response of 4 neighbouring columns.
Figure 2 shows the data collected in 4 neighbouring columns, respectively columns 94, 93, 92 and 91, running vertically and crossing the slanted edge (which has an angle of 15 deg.). Four SFRs are obtained, all with a relative low amount of data points. As illustrated in Figure 3, the amount of data points can be increased by means of multiplexing the 4 curves of Figure 2 into one single
SFR with 4 times the amount of samples.
Figure 3 : Spatial Frequency Response of the 4-times oversampled data, after multiplexing the 4 curves shown in Figure 2.
Based on this method of 4-times oversampling (also recommended by ISO 12233), the accuracy of the MTF measurement as a function of the angle of the slanted edge is checked again. The results of this exercise are shown in Figure 4.
Figure 4 : Effect of the slanted edge angle on the accuracy of the evaluation technique to characterize the MTF, based on a 4-times oversampling of the SFR data.
The result is quite remarkable : up to an angle of 20 deg. no deviation between the various obtained MTF curves can be seen, even not in the insert showing the MTF around the Nyquist frequency.
So oversampling when obtaining the SFR is absolutely recommendable, because it results in more data points to generate the SFR. And in the simulation result described in this and previous blogs, the “measured” modulatio n transfer function does not deviate from the theoretical one. Albert, 01-08-2014.
调制传递函数的测量与透镜像质评价
实验六 调制传递函数的测量与透镜像质评价 光学成像系统是信息传递的系统，光波携带输入图像的信息从物平面传播到像平面，输出像的质量完全取决于光学系统的传递特性。理想成像要求物平面与像平面之间一一对应。实际中，点物不能成点像，其原因就是通过成像系统后像质会变坏。传统的光学系统像质评价方法是星点法和鉴别率法，但它们均存在自身的缺点[1]。 20世纪50年代，霍普金斯（H ．H ．Hopkins ）提出了光学传递函数的概念，其处理方法是将输入图像看作由不同空间频率的光栅组成，通过研究这些空间频率分量在系统传递过程中丢失、衰减、相移等变化的情况，计算出光学传递函数的值并作出曲线来表征光学系统对不同空间频率图像的传递性能，这种方法是一种比较科学和全面的评价成像系统成像质量的方法。现在人们广泛用传递函数作为像质评价的判据，使质量评价进入客观计量。 一、实验目的 1．了解传递函数测量的基本原理，掌握传递函数测量和成像质量评价的近似方法； 2．通过对不同空间频率的矩形光栅成像的方法，测量透镜的调制传递函数。 二、实验原理 任何二维物体g(x, y)都可以分解成一系列沿x 方向和y 方向的不同空间频率(v x ，v y )的简谐函数(物理上表示正弦光栅)的线性叠加： (1) 式中Ｇ(v x ,v y ) 是物体函数g(x, y)的傅里叶谱，它表示物体所包含的空间频率 (v x ,v y ) 的成分含量，其中低频成分表示缓慢变化的背景和大的物体轮廓，高频成分则表征物体的细节。 当该物体经过光学系统后，各个不同频率的正弦信号发生两种变化：首先是对比度下降，其次是相位发生变化，而相应的Ｇ(v x ,v y )变为像的傅里叶谱()y x v v G ,'，这一综合过程可表示为： (2) 式中H (v x ,v y ) 称为光学传递函数，它是一个复函数，可以表示为： (3) 它的模m (v x , v y ) 被称为调制传递函数（modulation transfer function, MTF ），相位部分 φ (v x ，v y ) 则称为相位传递函数（phase transfer function, PTF ）。 对像的傅里叶谱() y x v v G ,' 再作一次逆变换，就得到像的复振幅分布： (４) 空间频率是用一种叫“光栅”的目标板来测试，它的线条从黑到白逐渐过渡，见图1。 ()()()[] y x y x y x dv dv y v x v i v v G y x g +=??∞∞-∞∞-π2exp ,,()()() y x y x y x v v H v v G v v G ,,,?='()()()[]y x y x y x dv dv y v x v i v v G y x g +-'='??∞∞-∞∞-π2exp ,,()()()[] y x y x y x v v j v v m v v H ,exp ,,φ=
传递函数的测量方法
传递函数的测量方法 一．测量原理 设输入激励为X （f ），系统（即受试的试件）检测点上的响应信号，即通过系统后在该响应 点的输出为Y (f )，则该系统的传递函数H (f )可以用下式表示： )() ()(f X f Y f H = 如果，设输入激励为X （f ）为常量k ，则该系统的传递函数H (f )可以用下式表示： )()(f kY f H = 也就是说，我们在检测点上测到的响应信号，就是该系统的传递函数。 二．测量方法 1. 将控制加速度传感器固定在振动台的工作台面上。注意：如果试件是通过夹具安装在振动台 的工作台面上，则控制加速度传感器应该安装在夹具与试件的连接点附近。如果试件与夹具的连 接是通过多个连接点固定，则应该选择主要连接点，或者采取多点控制的方法。 2. 将测量加速度传感器固定在选择的测量点（即响应点）上。 3. 试验采用正弦扫频方式，试验加速度选择1g ，扫频速率为0.5 Oct/min （或者更慢一些），试 验频率范围可以选择自己需要的频率范围。在试验中屏幕上显示的该激励曲线（也就是控制曲 线）应该是一条平直的曲线。这就保证对被测量试件来说是受到一个常量激励。 注意：在测量传递函数时，最好是采用线性扫频。因为，线性扫频是等速度扫频，这对于高频 段共振点的搜索比较好，能大大减少共振点的遗漏。而对于对数扫频来说，在低频段，扫频速 度比较慢；在高频段。扫频速度就比较快，这就有可能遗漏共振点。不少人之所以喜欢在测量 传递函数时采用对数扫频，是因为对于同样频率段的扫频来说，线性扫频要比对数扫频使用的 时间要多。 4. 通过控制仪，选择不同的颜色在屏幕上显示响应曲线。该响应曲线就是系统的频响曲线，在 这里也是该系统的传递函数曲线。注意：该控制仪可以在屏幕上同时显示好几条曲线。 三．其他方法 1. 测量原理 在闭环反馈控制时，为了保证控制点上被控制的物理量不变，当被控制的试件由于本身的 频率特性而将输入的激励信号放大时，从控制点上检测到的响应信号也将随着变大，也就是反馈 信号变大。由于，通常都是采取负反馈控制，那么，反馈信号与输入信号综合后再输入到系统中， 就会使控制点上的响应信号变小，而返回到原来的量级。 反过来，如果被控制的试件由于本身的频率特性而将输入的激励信号缩小时，从控制点上检 测到的响应信号也将随着变小，也就是反馈信号变小，那么，反馈信号与输入信号综合后再输入
光学传递函数的测量实验报告
实验四 光学传递函数测量和透镜像质评价 一. 实验目的 1. 了解光学镜头传递函数测量的基本原理； 2. 掌握传递函数测量和光学系统成像品质评价的近似方法 3. 学习抽样、平均和统计算法。 二. 主要仪器及设备 1. 导轨，滑块，调节支座，支杆，可调自定心透镜夹持器，干板夹； 2. 多用途三色LED 面光源； 3. 波形发生器，待测双凸透镜（Φ30，f120），待测双胶合透镜（Φ30，f90）； 4. CCD 及其稳压电源，CCD 光阑； 5. 图像采集卡及其与CCD 连线，微机及相应软件。 三. 实验原理 傅里叶光学证明了光学成像过程可以近似作为线形空间中的不变系统来处理，从而可以在频域中讨论光学系统的响应特性。任何二维物体ψo (x , y )都可以分解成一系列x 方向和y 方向的不同空间频率 (νx ,νy )简谐函数(物理上表示正弦光栅)的线性叠加： 式中ψo (νx ,νy )为ψo (x , y )的傅里叶谱，它正是物体所包含的空间频 率(νx ,νy )的成分含量，其中低频成分表示缓慢变化的背景和大的物体轮廓，高频成分则表征物体的细节。 当该物体经过光学系统后，各个不同频率的正弦信号发生两个变化：首先是调制度（或反差度）下降，其次是相位发生变化，这一综合过程可表为 []) 1(,)(2exp ),(),(o o y x y x y x d d y x i Ψy x ννννπννψ+= ??∞∞-∞ ∞-) 2(),,(),(),(o i y x y x y x ΨH Ψνννννν?=
)4( , min max min max A A A A m + - = [] y x y x y x d d i Ψν ν η ν ξ ν π ν ν η ξ ψ) ( 2 exp ) , ( ) , ( i i + =?? ∞ ∞ - ∞ ∞ - 式中ψi(νx,νy)表示像的傅里叶谱。H(νx,νy)称为光学传递函数，是一个复函数，它的模为调制度传递函数（modulation transfer function, MTF），相位部分则为相位传递函数（phase transfer function, PTF）。显然，当H=1时，表示像和物完全一致，即成像过程完全保真，像包含了物的全部信息，没有失真,光学系统成完善像。 由于光波在光学系统孔径光栏上的衍射以及像差（包括设计中的余留像差及加工、装调中的误差），信息在传递过程中不可避免要出现失真，总的来讲，空间频率越高，传递性能越差。 对像的傅里叶谱ψi(νx,νy)再作一次逆变换，就得到像的复振幅分布： (3) 调制度m定义为 式中A max和A min分别表示光强的极大值和极小值。光学系统的调制传递函数可表为给定空间频率下像和物的调制度之比： 除零频以外，MTF的值永远小于1。MTF(νx,νy)表示在传递过程中调制度的变化，一般说MTF越高，系统的像越清晰。平时所说的光学传递函数往往是指调制度传递函数MTF。图1给出一个光学镜头的设计MTF 曲线，不同视场的MTF不相同。 在生产检验中，为了提高效率，通常采用如下近似处理： 图1.光学传递函数（不同曲线对应于不同视场） )5( , ) , ( ) , ( ) , ( MTF o i y x y x y x m m ν ν ν ν ν ν=
C++中函数调用时的三种参数传递方式
在C++中，参数传递的方式是“实虚结合”。 ?按值传递(pass by value) ?地址传递(pass by pointer) ?引用传递(pass by reference) 按值传递的过程为：首先计算出实参表达式的值，接着给对应的形参变量分配一个存储空间，该空间的大小等于该形参类型的，然后把以求出的实参表达式的值一一存入到形参变量分配的存储空间中，成为形参变量的初值，供被调用函数执行时使用。这种传递是把实参表达式的值传送给对应的形参变量，故称这种传递方式为“按值传递”。 使用这种方式，调用函数本省不对实参进行操作，也就是说，即使形参的值在函数中发生了变化，实参的值也完全不会受到影响，仍为调用前的值。 [cpp]view plaincopy 1./* 2. pass By value 3.*/ 4.#include
如果在函数定义时将形参说明成指针，对这样的函数进行调用时就需要指定地址值形式的实参。这时的参数传递方式就是地址传递方式。 地址传递与按值传递的不同在于，它把实参的存储地址传送给对应的形参，从而使得形参指针和实参指针指向同一个地址。因此，被调用函数中对形参指针所指向的地址中内容的任何改变都会影响到实参。 [cpp]view plaincopy 1.#include
光学基础知识调制传输函数MTF解读
光学基础知识调制传输函数M T F解读 集团文件发布号：（9816-UATWW-MWUB-WUNN-INNUL-DQQTY-
光学基础知识：摄影镜头调制传输函数MTF解读 作者：老顽童 镜头是摄影师和摄影爱好者投资最高的设备之一，也是决定拍摄质量的最重要的因素。因此，镜头的质量，历来受到极大的重视。我们当然会很关心摄影镜头的测量方法。 摄影的最终产品是照片，所以，根据拍摄照片的质量来评价镜头质量，这是我们最先想到的，也是最基本的测试镜头的方法。实拍照片评价镜头质量的优点是结果直截了当，根据效果判断，比较放心。不过决定照片质量的客观因素很多，而一张照片的“好”与“坏”又需要人的主观判断，很难通过测量得出客观的定量结果。大量的事实表明，影响拍摄质量最重要的因素是镜头的分辨率和反差。反差大小可以通过仪器很容易测量，而分辨率就不那么容易了！现在我们经常采用拍摄标准分辨率板的方法测量镜头的分辨率。将拍摄了标准分辨率板的底片放到显微镜下人工判读，看最高能够分辩多少线条密度。分辨率的单位是线对/毫米(lp/mm)，一黑一白两条线算是一个线对，每毫米能够分辩出的线对数就是分辨率的数值。由于这种方法还是要受到胶片分辨率的客观影响和人工判读的主观影响，所以并不是最准确最理想的方法。 现在，让我们从另一个角度出发，将镜头看作一个信息传递系统：被拍摄景物反射出来的光线是它的输入信息，而胶片上的成像就是它的输出信息。一个优秀的镜头意味着它的输出的像忠实的再现了输入方景物的特性。喜欢音响的朋友都知道，高保真放大器的输出，应当准确地再现输入信号(图1)。当输入端输入频率变化而幅
度不变的正弦信号时，输出正弦波信号幅度的变化反映了放大器的频幅特性。频幅特性越平坦，放大器性能越好 (图2)！ 图1 放大器准确再现输入信号 图2 放大器的频幅特性 类似的方法也可以用来描述镜头的特性。由数学证明可知，任何周期性图形都可以分解成亮度按正弦变化的图形的叠加，而任何非周期图形又可以看作是周期图形片断的组合。因此，研究镜头对正弦变化的图形的反映，就可以研究镜头的性能！亮度按正弦变化的周期图形叫做“正弦光栅”。为了描述正弦光栅的线条密度，我们引入了“空间频率”的概念。一般正弦波的频率指单位时间(每秒钟)正弦波的周期数，对应的，正弦光栅的空间频率就是单位长度(每毫米)的亮度按照正弦变化的图形的周期数。
系统传递函数的测试方法 -随机信号实验
系统传递函数的测试方法 专业：通信工程 班级：010913 小组成员：陈娟01091312 陈欢01091264
摘要 随机信号在通信系统中有着重要的应用，信号处理技术及通信网络系统与计 算机网络的相互融合，都要求我们对研究分析电子系统受随机信号激励后的响应及测量方法有一个深入的了解。我们利用MATLAB仿真软件系统在数字信号处理 平台上进行系统仿真设计，并进行调试和数据分析，获得实验结果。 通信技术的广泛应用,也使其不得不面临各种环境的考验，本实验旨在通过matlab仿真产生理想高斯白噪声，利用互相关算法求取线性时不变系统的冲击响应，通过被测系统后的理想高斯白噪声信号与理想高斯白噪声信号进行互相关运算后产生一个信号a（t）。用matlab模拟低通滤波器和微分器，使a(t)通过该滤波器，获得线性系统单位冲击响应h(t)，分析该信号的均值、方差、相关函数、概率密度、频谱密度等数字特征。通过实验，可以了解matlab在系统仿真中的重要作用，并对电子系统受信号激励后的响应及测量方法有了一定的了解及认知。 关键词:互相关线性系统matlab
目录 一、实验目的 (4) 二、实验仪器 (4) 三、实验内容 (4) 四、实验步骤 (6) 高斯白噪声的导入 (6) 通过系统 (8) 通过被测系统后的信号与理想高斯白噪声进行互相关 (12) 通过低通滤波器得输出信号 (12) 五、计算x(t)、noise(t)、y(t)信号的均值（数学期望）、方差、相关函数、概率密度、频谱及功率谱密度等 (13) 1. noise(t)（白噪声） (13) 2. x(t) (15) 3. y(t) (17) 六、小结 (19) 七、参考文献 (19)
函数参数传递的原理
函数参数传递的原理 参数传递，是在程序运行过程中，实际参数就会将参数值传递给相应的形式参数，然后在函数中实现对数据处理和返回的过程，方法有按值传递参数，按地址传递参数和按数组传递参数。 形参：指出现在Sub 和Function过程形参表中的变量名、数组名，该过程在被调用前，没有为它们分配内存，其作用是说明自变量的类型和形态以及在过程中的作用。形参可以是除定长字符串变量之外的合法变量名，也可以带括号的数组名。 实参：实参就是在调用Sub 和Function过程时，从主调过程传递给被调用过程的参数值。实参可以是变量名、数组名、常数或表达式。在过程调用传递参数时，形参与实参是按位置结合的，形参表和实参表中对应的变量名可以不必相同，但它们的数据类型、参数个数及位置必须一一对应。 等号、函数名称、括弧和参数，是函数的四个组成部分。 函数“=SUM（1，2，3）”，1、2和3就是SUM函数的参数，没有参数1、2、3，函数SUM 则无从求值。 函数“=VLOOKUP（2，A:C，3，）”，没有参数2、A:C和3，函数VLOOKUP如何在A:C 区域查找A列中是2那一行第3列的数值？ 当然，也有不需要参数的函数，如“=PI（）”、“=NOW（）”、“TODAY（）”等。 函数参数传递的原理C语言中参数的传递方式一般存在两种方式：一种是通过栈的形式传递，另一种是通过寄存器的方式传递的。这次，我们只是详细描述一下第一种参数传递方式，另外一种方式在这里不做详细介绍。 首先，我们看一下，下面一个简单的调用例程： int Add （int a，int b，int c） { return a+b+c; }
(很实用,很好)用MATLAB 实现信号的调制与解调 调频 调相等
信号调制与解调 [实验目的] 1． 了解用MATLAB 实现信号调制与解调的方法。 2． 了解几种基本的调制方法。 [实验原理] 由于从消息变换过来的原始信号具有频率较低的频谱分量，这种信号在许多信道中不适宜传输。因此，在通信系统的发送端通常需要有调制过程，而在接收端则需要有反调制过程——解调过程。 所谓调制，就是按调制信号的变化规律去改变某些参数的过程。调制的载波可以分为两类：用正弦信号作载波；用脉冲串或一组数字信号作为载波。最常用和最重要的模拟调制方式是用正弦波作为载波的幅度调制和角度调制。本实验中重点讨论幅度调制。 幅度调制是正弦型载波的幅度随调制信号变化的过程。设正弦载波为 )c o s ()(o c t A t S ??+= 式中 c ?——载波角频率 o ?——载波的初相位 A ——载波的幅度 那么，幅度调制信号（已调信号）一般可表示为 )c o s ()()(o c m t t Am t S ??+= 式中，m(t)为基带调制信号。 在MATLAB 中，用函数y=modulate(x,fc,fs,’s’)来实现信号调制。其中fc 为载波频率，fs 为抽样频率，’s’省略或为’am -dsb-sc’时为抑制载波的双边带调幅，’am -dsb-tc’为不抑制载波的双边带调幅，’am -ssb ’为单边带调幅，’pm’为调相，’fm’为调频。 [课上练习] 产生AM FM PM signals [实验内容] 0. 已知信号sin(4) ()t f t t ππ= ，当对该信号取样时，求能恢复原信号的最大取样周期。
设计MATALB 程序进行分析并给出结果。 1． 有一正弦信号)256/2sin()(n n x π=, n=[0:256]，分别以100000Hz 的载波和 1000000Hz 的抽样频率进行调幅、调频、调相，观察图形。 2． 对题1中各调制信号进行解调（采用demod 函数），观察与原图形的区别 3． 已知线性调制信号表示式如下： ⑴ t t c ?cos cos Ω ⑵ t t c ?cos )sin 5.01(Ω+ 式中Ω=6c ?，试分别画出它们的波形图和频谱图 4． 已知调制信号)4000cos()200 cos()(t t t m ππ+=，载波为cos104t ，进行单边带调制，试确定单边带信号的表示式，并画出频谱图。 [实验要求] 1 自行编制完整的实验程序，实现对信号的模拟，并得出实验结果。 2 在实验报告中写出完整的自编程序，并给出实验结果和分析，学习demod 函数对调制信号进行解调的分析。 对1，2题解答，程序如下： clc;close all;clear; % Fm=10;Fs=1000;Fc=100;N=1000;k=0:N-1; % t=k/Fs; n=[0:256];Fc=100000;Fs=1000000;N=1000; xn=abs(sin(2*pi*n/256)); % x=abs(sin(2.0*pi*Fm*t));xf=abs(fft(x,N)); xf=abs(fft(xn,N)); y2=modulate(xn,Fc,Fs,'am'); subplot(211); plot(n(1:200),y2(1:200)); xlabel('时间(s)');ylabel('幅值');title('调幅信号'); yf=abs(fft(y2,N)); subplot(212);stem(yf(1:200));xlabel('频率(H)');ylabel('幅值');
光学传递函数的测量和像质评价
光学传递函数的测量和像质评价 引言 光学传递函数是表征光学系统对不同空间频率的目标函数的传递性能，是评价光学系统的指标之一。它将傅里叶变换这种数学工具引入应用光学领域，从而使像质评价有了数学依据。由此人们可以把物体成像看作光能量在像平面上的再分配，也可以把光学系统看成对空间频率的低通滤波器，并通过频谱分析对光学系统的成像质量进行评价。到现在为止，光学传递函数成为了像质评价的一种主要方法。 一、实验目的 了解光学镜头传递函数的基本测量原理，掌握传递函数测量和成像品质评价的近似方法，学习抽样、平均和统计算法，熟悉光学软件的应用。 二、基本原理 光学系统在一定条件下可以近似看作线性空间中的不变系统，因此我们可以在空间频率域来讨论光学系统的响应特性。其基本的数学原理就是傅里叶变换和逆变换，即： dxdy y x i y x )](2exp[,ηξπψηξψ+-=??） （），（ （1） ηξηξπηξψψd d y x i y x )](2exp[),(),(+=?? （2） 式中),(ηξψ是),(y x ψ的傅里叶频谱，是物体所包含的空间频率),(ηξ的成分含量，低频成分表示缓慢变化的背景和大的轮廓，高频成分表示物体细节，积分范围是全空间或者是有光通过空间范围。 当物体经过光学系统后，各个不同频率的正弦信号发生两个变化：首先是调制度（或反差度）下降，其次是相位发生变化，这一综合过程可表为 ），（），（），（ηξηξψηξφH ?= （3） 式中），（ηξφ表示像的傅里叶频谱。），（ηξH 成为光学传递函数，是一个复函数，它的模为调制度传递函数（modulation transfer function, MTF ），相位部分则为相位传递函数（phase transfer function, PTF ）。显然，当H =1时，表示象和物完全一致，即成象过程完全保真，象包含了物的全部信息，没有失真,光学系统成完善象。由于光波在光学系统孔径光栏上的衍射以及象差（包括设计中的余留象差及加工、装调中的误差），信息在传递过程中不可避免要出现失真，总的来讲，空间频率越高，传递性能越差。要得到像的复振幅分布，只需要将像的傅里叶频谱作一次逆傅里叶变换即可。 在光学中，调制度定义为 min max min max I I I I m +-= (4) 式中max I 、min I 表示光强的极大值和极小值。光学系统的调制传递函数可表为给定空间频率
基于调制函数的SVPWM算法
2008年 2 月电工技术学报Vol.23 No.2 第23卷第2期TRANSACTIONS OF CHINA ELECTROTECHNICAL SOCIETY Feb. 2008 基于调制函数的SVPWM算法 陆海峰1瞿文龙1张磊1张星1樊扬1程小猛1 靳勇刚2肖波2 （1. 清华大学电机工程与应用电子技术系电力系统国家重点实验室北京 100084 2. 中国南车集团株洲电力机车研究所株洲 412001） 摘要为了避免复杂的三角函数和求根运算，便于数字信号处理器的实时运算，提出一种新的SVPWM算法。采用SPWM中调制波与载波相比较的规则采样思路，通过在静止坐标系下直接计算每个参考电压矢量所对应的三相调制波的函数值，进而得到每相电压在一个PWM周期中的占空比。该算法的主要特点是计算简单，只需要普通的四则运算, 适用于数字化系统。在扇区划分和占空比饱和的处理上较传统SVPWM算法更简便，且过调制范围也略有拓展，具有很大的实用性。仿真和实验结果证实了该算法的有效性。 关键词：电压型逆变器空间矢量脉宽调制异步电动机调制函数过调制 中图分类号：TM 464 SVPWM Algorithm Based on Modulation Functions Lu Haifeng1 Qu Wenlong1 Zhang Lei1 Zhang Xing1 Fan Yang1 Cheng Xiaomeng1 Jin Yonggang2 Xiao Bo2 （1. Tsinghua University Beijing 100084 China 2. Zhuzhou Electric Locomotive Research Institute Zhuzhou 412001 China） Abstract In order to avoid complex calculation of triangle functions and square root, and realize feasibly real-time calculation by DSP, a new space vector pulse width modulation(SVPWM) algorithm is developed. Coming from the idea of SPWM regular sampling in which the modulated wave compares with carrier, by directly calculating the corresponding three-phase modulated wave function values of the reference voltage vector in the static frame, the PWM duty ratio of every phase voltage is then obtained. The principle of the algorithm is introduced and the formulas of PWM calculation are derived in the paper. It just contains the four fundamental arithmetic operations, and it is suitable in the digital systems. In addition, it is more convenient than traditional PWM calculation in the sector dividing and the duty ratio saturation dealing, and the range of over-modulation is some few extended. So the algorithm has good practicality. The results of simulation and experiment verify the validity of the method. Keywords：Voltage source inverter (VSI), space vector pulse width modulation (SVPWM), induction motor, modulation function, over modulation 1引言 随着电力电子技术和微处理器的发展，脉宽调制（Pulse Width Modulation，PWM）技术在电力传动领域得到了广泛应用。在各种PWM技术中，空间矢量PWM（Space Vector PWM，SVPWM）技术以其调制比高和易于数字化的优点，在高性能全数字化交流调速系统中得到了较多应用[1-2]。 在一般的数字化系统中，其CPU（如单片机或 国家“863”高技术项目（2005AA501130）。收稿日期 2007-01-26 改稿日期 2007-4-20
光学基础知识调制传输函数MTF解读
光学基础知识：摄影镜头调制传输函数MTF解读 作者：老顽童 镜头是摄影师和摄影爱好者投资最高的设备之一，也是决定拍摄质量的最重要的因素。因此，镜头的质量，历来受到极大的重视。我们当然会很关心摄影镜头的测量方法。 摄影的最终产品是照片，所以，根据拍摄照片的质量来评价镜头质量，这是我们最先想到的，也是最基本的测试镜头的方法。实拍照片评价镜头质量的优点是结果直截了当，根据效果判断，比较放心。不过决定照片质量的客观因素很多，而一张照片的“好”与“坏”又需要人的主观判断，很难通过测量得出客观的定量结果。大量的事实表明，影响拍摄质量最重要的因素是镜头的分辨率和反差。反差大小可以通过仪器很容易测量，而分辨率就不那么容易了！现在我们经常采用拍摄标准分辨率板的方法测量镜头的分辨率。将拍摄了标准分辨率板的底片放到显微镜下人工判读，看最高能够分辩多少线条密度。分辨率的单位是线对/毫米(lp/mm)，一黑一白两条线算是一个线对，每毫米能够分辩出的线对数就是分辨率的数值。由于这种方法还是要受到胶片分辨率的客观影响和人工判读的主观影响，所以并不是最准确最理想的方法。 现在，让我们从另一个角度出发，将镜头看作一个信息传递系统：被拍摄景物反射出来的光线是它的输入信息，而胶片上的成像就是它的输出信息。一个优秀的镜头意味着它的输出的像忠实的再现了输入方景物的特性。喜欢音响的朋友都知道，高保真放大器的输出，应当准确地再现输入信号(图1)。当输入端输入频率变化而幅度不变的正弦信号时，输出正弦波信号幅度的变化反映了放大器的频幅特性。频幅特性越平坦，放大器性能越好(图2)！ 图1 放大器准确再现输入信号
图2 放大器的频幅特性 类似的方法也可以用来描述镜头的特性。由数学证明可知，任何周期性图形都可以分解成亮度按正弦变化的图形的叠加，而任何非周期图形又可以看作是周期图形片断的组合。因此，研究镜头对正弦变化的图形的反映，就可以研究镜头的性能！亮度按正弦变化的周期图形叫做“正弦光栅”。为了描述正弦光栅的线条密度，我们引入了“空间频率”的概念。一般正弦波的频率指单位时间(每秒钟)正弦波的周期数，对应的，正弦光栅的空间频率就是单位长度(每毫米)的亮度按照正弦变化的图形的周期数。 图3 正弦光栅 典型的正弦光栅如图3所示。相邻的两个最大值的距离是正弦光栅的空间周期，单位是毫米。空间周期的倒数就是空间频率(Spatial Frequency)，单位是线对/毫米(lp/mm，linepairs/mm)。正弦光栅最亮处与最暗处的差别，反映了图形的反差(对比度)。设最大亮度为Imax，最小亮度为Imin，我们用调制度(Modulation)表示反差的大小。调制度M定义如下： M=(Imax－Imin)/(Imax＋Imin) 很明显，调制度介于0和1之间。调制度越大，意味着反差越大。当最大亮度与最小亮度完全相等时，反差完全消失，这时的调制度等于0。 我们将正弦光栅置于镜头前方、在镜头成像处测量像的调制度，发现当光栅空间频率很低时，像的调制度几乎等于正弦光栅的调制度；随着空间频率的提高，像的调制度逐渐单调下降；空间频率高到一定程度，像的调制度逐渐降低到0、完全失去了反差！ 正弦信号通过镜头后，它的调制度的变化是正弦信号空间频率的函数，这个函数称为调制传递函数MTF(Modulation Transfer Function)。对于原来调制度为M的正弦光栅，如果经过镜头到达像平面的像的调制度为M ’ ，则MTF函数值为： MTF值= M ’ / M 可以看出，MTF值必定介于0和1之间，并且越接近1、镜头的性能越好！ 如果镜头的MTF值等于1，镜头输出的调制度完全反映了输入正弦光栅的反差；而如果输入的正弦光栅的调制度是1，则输出图像的调制度正好等于MTF值！所以，MTF函数代表了镜头在一定空间频率下的反差。
光学传递函数的测量和评价解读
光学传递函数的测量和评价 引言 光学传递函数是表征光学系统对不同空间频率的目标函数的传递性能,是评价光学系统 的指标之一。它将傅里叶变换这种数学工具引入应用光学领域,从而使像质评价有了数学依据。由此人们可以把物体成像看作光能量在像平面上的再分配,也可以把光学系统看成对空间频率的低通滤波器,并通过频谱分析对光学系统的成像质量进行评价。到现在为止,光学传递函数成为了像质评价的一种主要方法。 一、实验目的 了解光学镜头传递函数的基本测量原理,掌握传递函数测量和成像品质评价的近似方 法,学习抽样、平均和统计算法,熟悉光学软件的应用。 二、基本原理 光学系统在一定条件下可以近似看作线性空间中的不变系统,因此我们可以在空间频率域来讨论光学系统的响应特性。其基本的数学原理就是傅里叶变换和逆变换,即: dxdy y x i y x ](2exp[,ηξπψηξψ+-=?? (,( (1 ηξηξπηξψψd d y x i y x ](2exp[,(,(+=?? (2 式中,(ηξψ是,(y x ψ的傅里叶频谱,是物体所包含的空间频率,(ηξ的成分含量,低频成分表示缓慢变化的背景和大的轮廓,高频成分表示物体细节,积分范围是全空间或者是有光通过空间范围。
当物体经过光学系统后,各个不同频率的正弦信号发生两个变化:首先是调制度(或反 差度下降,其次是相位发生变化,这一综合过程可表为 ,(,(,(ηξηξψηξφH ?= (3 式中,(ηξφ表示像的傅里叶频谱。,(ηξH 成为光学传递函数,是一个复函数, 它的模为调制度传递函数(modulation transfer function, MTF ,相位部分则为相位传递函数(phase transfer function, PTF 。显然,当H =1时,表示象和物完全一致,即成象过程完全保真,象包含了物的全部信息,没有失真,光学系统成完善象。由于光波在光学系统孔径光栏上的衍射以及象差(包括设计中的余留象差及加工、装调中的误差,信息在传递过程中不可避免要出现失真,总的来讲,空间频率越高,传递性能越差。要得到像的复振幅分布,只需要将像的傅里叶频谱作一次逆傅里叶变换即可。 在光学中,调制度定义为 min max min max I I I I m +-= (4 式中max I 、min I 表示光强的极大值和极小值。光学系统的调制传递函数可表为给定空间频率 下像和物的调制度之比: (ηξ,M TF = ,(,(ηξηξo i m m 一般说来,MTF 越高,系统像越清晰,我们说光学传递函数往往就是指调制传递函数。调制 传递函数随视场变化而变化,我们可以通过调制传递函数的各个不同值来评价光学系统的成 像质量。
光学传递函数测试仪的现状和发展趋势
文章编号!"##$%$&’#()##’*#$%##+,%#$ 光学传递函数测试仪的现状和发展趋势- 樊翔.倪旭翔 (浙江大学国家光学仪器工程技术研究中心.浙江杭州’"##)/* 摘要!光学传递函数被公认为目前评价光学系统成像质量比较客观0有效的方法1给出光学传递函数的基本理论.介绍了目前国内外主要光学传递函数测试仪的数学模型0测试 原理0基本结构和主要性能.并阐述了今后光学传递函数测试仪的发展趋势1 关键词!光学传递函数2测试仪2现状2发展趋势 中图分类号!34/+文献标识码!5 67898:;9;<;=9<:>>8?8@A B C8:;;78:>A D E F G;89;H:IH:9;7=C8:; J5K L M N O P.KQ L R S T M N O P (U V W X UY Z[\]^_‘a b c d e^[f g h d^.i j h k_a d lm d_n h[e_^o.p a d l q j Z f’"##)/.U j_d a* r s9;7
数字式光学传递函数测量和透镜象质评价
实验八 数字式光学传递函数的测量和像质评价实验 1．实验目的 了解光学镜头传递函数测量的基本原理； 掌握传递函数测量和成像品质评价的近似方法； 学习抽样、平均和统计算法。 2. 基本原理 光学传递函数（Optical transfer function, OTF ）表征光学系统对不同空间频率目标的传递性能，广泛用于对系统成像质量的评价。 傅里叶光学证明了光学成像过程可以近似作为线形空间中的不变系统来处理，从而可以在频域中讨论光学系统的响应特性。任何二维物体ψo (x , y )都可以分解成一系列x 方向和y 方向的不同空间频率(f x ,f y )简谐函数(物理上表示正弦光栅)的线性叠加： o o (,)(,)exp 2(),(1)x y x y x y x y f f i f x f y df df ψπ∞∞ -∞-∞??= Φ+???? 式中Φo (f x ,f y )为ψo (x , y )的傅里叶谱，它正是物体所包含的空间频率(f x ,f y )的成分含量，其中低频成分表示缓慢变化的背景和大的物体轮廓，高频成分则表征物体的细节。 当该物体经过光学系统后，各个不同频率的正弦信号发生两个变化：首先是调制度（或反差度）下降，其次是相位发生变化，这一综合过程可表为 i o (,)(,)(,),(2)x y x y x y f f H f f f f Φ=?Φ 式中Φi (f x ,f y )表示像的傅里叶谱。H (f x ,f y )称为光学传递函数，是一个复函数，它的模为调制度传递函数（modulation transfer function, MTF ），相位部分则为相位传递函数（phase transfer function, PTF ）。显然，当H =1时，表示像和物完全一致，即成像过程完全保真，像包含了物的全部信息，没有失真,光学系统成完善像。 由于光波在光学系统孔径光栏上的衍射以及像差（包括设计中的余留像差及加工、装调中的误差），信息在传递过程中不可避免要出现失真，总的来讲，空间频率越高，传递性能越差。 对像的傅里叶谱Φi (f x ,f y )再作一次逆变换，就得到像的复振幅分布：
数字式光学传递函数测量和透镜象质评价
数字式光学传递函数的测量和像质评价实 验 实验讲义 大恒新纪元科技股份有限公司 版权所有不得翻印
) 4(,min max min max A A A A m +-=[]y x y x y x d d i Ψννηνξνπννηξψ)(2exp ),(),(i i +=??∞∞-∞∞-数字式光学传递函数的测量和像质评价实验 1.引言 光学传递函数（Optical transfer function, OTF ）表征光学系统对不同空间频率的目标的传递性能，广泛用于对系统成像质量的评价。 2．实验目的 了解光学镜头传递函数测量的基本原理，掌握传递函数测量和成像品质评价的近似方法，学习抽样、平均和统计算法。 3. 基本原理 傅里叶光学证明了光学成像过程可以近似作为线形空间中的不变系统来处理，从而可以在频域中讨论光学系统的响应特性。任何二维物体ψo (x , y )都可以分解成一系列x 方向和y 方向的不同空间频率(νx ,νy )简谐函数(物理上表示正弦光栅)的线性叠加： 式中ψo (νx ,νy )为ψo (x , y )的傅里叶谱，它正是物体所包含的空间频率(νx ,νy )的成分含量，其中低频成分表示缓慢变化的背景和大的物体轮廓，高频成分则表征物体的细节。 当该物体经过光学系统后，各个不同频率的正弦信号发生两个变化：首先是调制度（或反差度）下降，其次是相位发生变化，这一综合过程可表为 式中ψi (νx ,νy )表示像的傅里叶谱。H (νx ,νy )称为光学传递函数，是一个复函数，它的模为调制度传递函数（modulation transfer function, MTF ），相位部分则为相位传递函数（phase transfer function, PTF ）。显然，当H =1时，表示像和物完全一致，即成像过程完全保真，像包含了物的全部信息，没有失真,光学系统成完善像。 由于光波在光学系统孔径光栏上的衍射以及像差（包括设计中的余留像差及加工、装调中的误差），信息在传递过程中不可避免要出现失真，总的来讲，空间频率越高，传递性能越差。 对像的傅里叶谱ψi (νx ,νy )再作一次逆变换，就得到像的复振幅分布： (3) 调制度m 定义为 []) 1(,)(2exp ),(),(o o y x y x y x d d y x i Ψ y x ννννπννψ+=??∞∞-∞ ∞-) 2(),,(),(),(o i y x y x y x ΨH Ψνννννν?=