随机相位导致相干斑
一副影像的相位是随机的，原因：
One pixel of a radar image usually represents a surface of several tens of square meters, containing numerous elementary targets (stones, branches, etc.). These targets all contribute to the signal and are located at different ranges from the radar.
Since the wavelength is much smaller than the size of the pixel, the phase of a given target may be shifted by any value. The combination of these targets further randomizes the phase of the pixel. Clearly, no one value is statistically more significant than another.
As far as amplitude is concerned, the contributions of two identical targets found in the same pixel can reinforce each other if their phases are identical or cancel each other out if they are opposite.
The summing of the random phase values of these various targets produces the phenomenon known as ‘speckle’. If the same targets were arranged differently in another pixel they might produce a significantly different amplitude and an unpredictably different phase.
所以这样的相位信息没有办法加以利用，不过，两个这样的影像或许可以：
If we want to use the phase of the signal as a measuring technique, the trick is above all to fully comprehend what is meant by ‘random’. A pixel phase is random because we do not know where the elementary targets are located within it.
But on a second pass over the same pixel in exactly the same conditions we would of course obtain the same phase.
Interferometry depends on the idea that, instead of using the phase of a radar image to measure the ranges, we can use the difference of phase between two radar images to measure differences or geometric distortions in range between these two images.
We therefore count on the fact that the complex contribution depending on the particular arrangement of elementary targets in each pixel will be cancelled by combining the two images.
突然之间，我们会喜欢上这种随机，但是，我们希望这种随机在两幅影像上一致，只有这样才能够相互抵消，要不然仍然是可怕的随机。（就像上帝掷骰子一样，随机性有时候会让人觉得恐怖。）
这种能够”be cancelled”的能力，另一种说法就是相干。
事实上两幅影像是不可能“in exactly the same conditions”的：
The two images which are merged point by point to form the image of their phase differences, called an interferogram, usually have different viewpoints because they were not taken from exactly the same place, and a time shift because they were not taken at the same moment.
These two differences are almost always found in an interferogram. There may be no time difference in the case of systems with two radar antennas which can create two images simultaneously. In certain circumstances there may be no difference in viewpoint, if a satellite repasses at almost exactly the same point when acquiring the second image.
These two differences are the source of the two types of information provided by interferometry. The difference of viewpoint provides the topographical information in the interferogram. The time difference provides information on displacement.
最后说说相干斑speckle:
Homogeneous areas of terrain that extend across many SAR resolution cells (imagine, for example, a large agricultural field covered by one type of cultivation) are imaged with different amplitudes in different resolution cells. The visual effect is a sort of ‘salt and pepper’ screen superimposed on a uniform amplitude image.
This speckle effect is a direct consequence of the superposition of the signals reflected by many small elementary scatterers (those with a dimension comparable to the radar wavelength) within the resolution cell. These signals, which have random phase because of multiple reflections between scatterers, add to the directly reflected radiation. From an intuitive point of view, the resulting amplitude will depend on the imbalance between signals with positive and negative sign.
对付相干斑的办法：
Typically, image segmentation suffers severely from speckle. However, by taking more images of the same area at different times or from slightly different look angles, speckle can be greatly reduced: averaging several images tends to cancel out the random amplitude variability and leave the uniform amplitude level unchanged.
但这个方法能否用在干涉之前呢？似乎不能，是不是可能破坏掉相位信息？
相干与critical baseline
上面提到：这种能够”be cancelled”的能力，另一种说法就是相干。
实际上，衡量这种能力的指标叫相干系数。
An InSAR coherence image is a cross-correlation product derived from two co-registered complex-valued (both intensity and phase components) SAR images. It depicts changes in backscattering characteristics on the scale of the radar wavelength. Loss of InSAR coherence is often referred to as decorrelation.
相干性跟许多因素有关，其中一种是，基线，（垂直）基线越长，相干性会下降，当相干性完全消失时对应的垂直基线是critical baseline。这个定义还有很多其他的推导方式。它与波长、斜距、带宽、倾角、坡度角和光速有关。
关于critical baseline，另外一种解释方式，一个像素内部的各个目标的相位变化不应该因为基线（过大）而发生超过一个周期的差异：
Let us take two distinct targets A and B, located at opposite edges of the same pixel in a reference image (one near the radar, the second further away). Targets A and B are indistinguishable within the pixel. Any elementary target in the pixel is subject to phase variations when passing from one image to another.
The phase difference of the same pixel in M and S should not depend too much on the position of the target within the pixel. For instance, the phase difference itself should vary by much less than a full cycle between A and B.
The overall phase difference resulting from the mixing of points P at various locations in the pixel will be insignificant at the scale of the pixel as long as the difference in δ (called the horizontal baseline) remains less than a limiting value. If this is not the case, the phase difference between the two images will again be the result of contributions which are random since they can vary within the pixel itself by more than a cycle. It will then be impossible to exploit this phase difference.
For the limiting case where the targets are located at opposite edges of the pixel, the stability of the phase difference will be guaranteed by the stability of the incidence angle of the wave between the two images. Should this change too much, the path difference between the two targets in one image will differ from the path difference in the other image by more than a wavelength, resulting in a pure random difference of phase. For example, a 10-m ground pixel observed from an incidence angle of 30 implies a round trip path difference of 10 m between two targets at opposite edges of the pixel. If we wish to limit the variation of this path difference to a fraction of the wavelength, for example 1 cm, then the incidence angle in the second image must be between 29.967 and 30.033
A clearer way of quantifying this condition is to express the maximum acceptable horizontal distance δ between the points from which the images are acquired (also called the horizontal critical baseline, and deduced from the critical orthogonal baseline). For a satellite like ERS orbiting at an altitude of approximately 1000 km, this distance δ is about 1 km. In practice, we can only combine images separated by an integer number of satellite orbital cycles. The satellite is supposed to return to exactly the same position after each cycle. In most cases, it is actually less than 1 km away.
Critical baseline 的第三种解释方式是主辅影像间的距离向频谱偏移
相位噪声
与相干性有关的另一个概念是相位噪声phase noise，这跟上面的问题其实联系得非常紧密，毕竟一幅影像也是复数，也是包括大小和相位的。
In the previous sections it has been hypothesised that only one dominant stable scatterer was present in each resolution cell. This is seldom the case in reality. We should analyse the situation where many elementary scatterers are present in each resolution cell (distributed scatterers), each of which may change in the time interval between two SAR acquisitions. The main effect of the presence of many scatterers per resolution cell and their changes in time is the introduction of phase noise. Three main contributions to the phase noise should be taken into consideration:
关于第二个，没错，基线会带来相位噪声，但是正是因为基线的存在，才能够进行地形测量。这里的spectral shift 方法在处理相位噪声的时候，会不会影响到有用的干涉相位？
P45（靳）中分析得到的频谱相差正是能够进行地形测量的原因吧？应该不能完全去除？
答，这里的相位噪声来自于：the different combination of elementary （一个像素之内的），所以这里是不是只是在尽力去除掉一个像素内部的频谱偏移呢？（P18 practical approach）
还是说频谱偏移本身就是个坏东西，应该完全避免，我们的干涉测量并不会利用到频谱偏移？（仔细想想干涉测量的原理，根本原理是距离差对应相位差，跟频率似乎没有什么关系。另一方面，频率的变化势必会造成相位的变化，也就是说记录数据的相位不准确。）
**以上的解释见“Range spectral shift”部分：
这个频谱偏移会导致失相关 是个坏东西 应该消灭掉
他代表的是相位随着斜距的变化 是由于视角差造成的
如果没有视角差 就没有干涉相位（或者说干涉相位是零，这里不考虑形变） 自然也就没有干涉相位的变化
这个视角差使得我们能够通过干涉相位进行地形测绘，但她同时导致了干涉相位的变化这个“副产品”。我们应该消除掉这个副产品，他和干涉相位不是一回事儿。**
The phase noise can be estimated from the interferometric SAR pair by means of the local coherence γ. The local coherence is the cross-correlation coefficient of the SAR image pair estimated over a small window (a few pixels in range and azimuth), once all the deterministic phase components (mainly due to the terrain elevation) are compensated for.
The deterministic phase components in such a small window are, as a first approximation, linear both in azimuth and slant-range. Thus, they can be estimated from the interferogram itself by means of well-known methods of frequency detection of complex sinusoids in noise (e.g. 2-D Fast Fourier Transform (FFT)).
The coherence map of the scene is then formed by computing the absolute value of γ on a moving window that covers the whole SAR image.
相位噪声（The phase dispersion）可以表达为相干系数γ的函数，The phase dispersion can be exploited to estimate the theoretical elevation dispersion (limited to the high spatial frequencies) of a DEM generated from SAR interferometry.
相位噪声、相干、滤波、以及 covariance matrix estimation 之间的关系 将在后续详细分析。