Sunlight and Moonlight are coherent or not? I have tried a lot to find the exact answer for this question but unfortunately couldn't get it. If Sunlight and Moonlight are coherent then What could be the reason behind this?
 A: After search the web, I found the the van Cittert-Zernike Theorem,
https://www.physics.purdue.edu/webapps/index.php/course_document/index/phys322/1460/25/11076
that states that the spatial coherence area $A_c$ is given by: 
$$A_c=\frac{D^2 \lambda^2}{\pi d^2}$$
where $d$ is the diameter of the light source and $D$ is the distance away.
For sunlight, $D = 150\cdot 10^9\text{ m}$, $\lambda=5\cdot 10^{-7}\text{ m}$, $d=1.4\cdot 10^9\text{ m}$.
$A_c= 9\cdot 10^{-10}\text{ m}^2$,
$L = Ac^{0.5} = 3\cdot 10^{-5}\text{ m}$
This result says light is not coherent over most distances.  However, phenomenon such as glint I believe are based on coherent light reflecting off surfaces of several cm of length, so this is not the results I expected. 
Let's explore this further. The directivity of an antenna, which is approximately equal to the coherent gain is given by
$D_{\text{coh}}=\frac{4\pi A}{\lambda^2}$. Using the previous calculations
$D_{\text{coh}}=4.5\cdot 10^4$;
A lower bound for noncoherent directivity is $N^{0.5}$ versus $N$ for coherent directivity. This means $D_{\text{noncoherent}} < 4\pi(A/\lambda^2)^{0.5}$.  This results in
$D_{\text{non_coh}}=750$;
Their ratio $= D_{coh}/D_{non_coh}$, which is gain enhancement due to coherence is $60$, but it could be less. I think $60$ times more brighter is significant, so glint makes sense according to these results. Big glint surfaces would be a combination of coherent and non coherent scattering, which add gain. This seems reasonable. These results do not take into account turbulence in the atmosphere, which may not matter for $L = 3\cdot 10^{-5}\text{ m}$.  Not sure.
Do these calculations make sense? I am not an expert.
A: Although I am not an expert, I am tempted to enlarge on the comments given above.  I hope it is all right that I go back to basics.
My gut reaction would be to say that sunlight and moonlight are incoherent in themselves,  and even more so in relation to each other.  Moonlight is perhaps less coherent than sunlight because it is a diffuse reflection from the surface of the moon.  But putting my gut reaction aside,  as pointed out by dmckee, coherence of light is a question of degree,  the degree of coherence being computed by complicated formulae or measured by optical experiments.
The concept of coherence is connected to how easily a beam of light can be made to interfere with itself.  Let us consider a screen with two small holes illuminated by sunlight.  The holes will give two patches of light on a receiving screen put a little behind the first screen.  Where the two patches overlap, we may see black and white stripes, interference fringes.  The contrast of these fringes depends on the distance between the holes.   If the holes are far apart, there will be no stripes,  but as the holes get closer to each other, stripes appear with increasing contrast.  It has been found for sunlight that the holes have to be as close as 0.02 mm before we obtain a reasonable contrast of the stripes.  I feel that this is very close, and it indicates a low degree of coherence.  This type of coherence is called  "spatial coherence" because it depends upon the coherence of the beam at different places.
A Michelson interferometer  is  another way of making the beam interfere with itself.  The beam is split in two parts by a half-silvered mirror, and recombined to interfere by other mirrors.  The length of the paths followed by each beam can be adjusted by moving the mirrors.  If the difference in path length is small or zero, we can again see interference fringes. The contrast depends on the difference in path length between the two beams, and the fringes disappear if the path difference is too large.  This gives rise to the concept "coherence length".  I have no value for sunlight,  but the coherence length is connected to how many different wavelengths of light are present in sunlight, the width of the solar spectrum.  Sunlight has a very wide spectrum, so the coherence length should be quite small, indicating a low degree of coherence.  This kind of coherence is called "temporal coherence", because it depends on the difference in time the light has used to traverse the two paths. 
It is interesting to note that knowledge of even the small coherence of sunlight may be important in designing modern solar cells with high efficiency.
