From 494f181c0037a62701180ac1381b6d0704dca709 Mon Sep 17 00:00:00 2001 From: petergu Date: Wed, 4 Nov 2020 21:11:44 +0800 Subject: [PATCH] image_in_lab: update --- official/来自一教的图片/README.md | 29 +++++++++++++++++++++++++++++ official/来自一教的图片/pic/1.png | Bin 0 -> 171409 bytes official/来自一教的图片/pic/2.png | Bin 0 -> 1100426 bytes 3 files changed, 29 insertions(+) create mode 100644 official/来自一教的图片/pic/1.png create mode 100644 official/来自一教的图片/pic/2.png diff --git a/official/来自一教的图片/README.md b/official/来自一教的图片/README.md index 751ff85..d376cb3 100644 --- a/official/来自一教的图片/README.md +++ b/official/来自一教的图片/README.md @@ -1 +1,30 @@ # 来自一教的图片 + +对图像二维傅里叶变换就结束了。灵感来自于三级大学物理实验“傅里叶光学”。 + +用 Python 的解法: + +```python +import numpy as np +import cv2 as cv +from matplotlib import pyplot as plt +img = cv.imread('./4f_system_middle.bmp', 0) +f = np.fft.fft2(img) +logf = 20*np.log(np.abs(f)) +plt.imshow(logf, 'gray') +``` + +![1](pic/1.png) + +注意 Python 变换之后可能会有一个点值非常大,画图时导致剩下的图像看不出来,手动修复或对数做图(这也是 FFT 的基本操作)即可。对于(逆)变换之后得到的 f ,做图时取实部还是虚部还是模可能需要都试一下,比如取实部只能看到一点线条,取模就能很好地看到图像,但这个应该也不难想到。 + +用商业软件 Mathematica 的解法: + +![2](pic/2.png) + +嗯,就这样结束了。 + +题目中傅里叶光学是提示,文件名意思是 4F 成像系统中间,就对应物的傅里叶变换平面,也算是提示了,但或许对非物理专业的同学还是有点脑洞吧。 + +为什么题目中说是模拟呢,因为题目中的图片取的是物傅里叶变换的实部,而一般实验能直接观测光强和相位分布,看电场实部或者虚部还真没听说过。这么做的原因是衍射(就是 FFT ,可见参考[ Matlab 官方文档](https://www.mathworks.com/help/matlab/math/two-dimensional-fft.html))光强分布不同地方差几个量级,如果这样存到图片里就损失了大量的信息。就算取了实部其实强度信息也基本损失完了,所以图片上除了黑点就是白点,几乎没有中间颜色,但因为实部包含了相位信息,所以仍能成功重构图像,因为[图像的细节信息其实在相位而不是强度中](https://people.eecs.berkeley.edu/~sastry/ee20/vision2/node6.html)。 + diff --git a/official/来自一教的图片/pic/1.png b/official/来自一教的图片/pic/1.png new file mode 100644 index 0000000000000000000000000000000000000000..8e8240e444ff6676d3e2aba2fe92f4ff51254025 GIT binary patch literal 171409 zcmeFYg;$jC7d@)v5CTJklX7hT zd#d0$@c0*gPl*3}3|&YQ1`bNAySo29Yc_=ML)icOfBeXYShp>6&VCO)=(to3vh^jA zsVAAc=j1P5?&{NK-#Z)Rh5dW_blC5YeUFx@-S2nX19lk}o>njU-}7x@W}2OhYs%q!v 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