# Diffraction Pattern on LCD Screen

I was up late working with my red LED headlamp on and when I was looking at the black part of my LCD (Apple Retina Macbook Pro) screen I noticed this interesting diffraction pattern. I'm confused because all I can think of that would cause this are Fourier and Fraunhofer patterns which I thought required more advanced optics the light to be collimated. One friend suggested it might be the polarizer. Any thoughts?

Unfortunately, the picture doesn't show this, but along the x and y axes there were discrete points not a continuous streak. Sorry for the horrible photo quality. • It has nothing to do with diffraction, just the fact that LED cells only let light reflect in vertical and horizontal directions (because cells are squares or rectangles), not really diagonally. This is my line of thought, when I see these patterns. I think, same happens when you look on a street lamp through the bug net on the window. – aaaaa says reinstate Monica Mar 2 '15 at 8:51
• That was what occurred to me at first. However, the pattern only occurs on the LCD screen. I tried pointing the light at a variety of surfaces and the LED light only showed the pattern on the LCD. All the other surfaces just had a pattern similar to a conventional light. Also, the discrete light points are vary with distance to the screen so it's not just individual pixels causing the pattern. – lswim Mar 2 '15 at 8:53
• You might be interested in this question and my answer thereto - going a little deeper into the phenomenon of diffraction from and LCD screen. – Floris Jan 29 '17 at 4:07

The diffraction seems to form from the pixels (basically a diffraction grating). The pixels have a translational symmetry in $x$ and $y$ directions, so the pattern also exhibits this symmetry. On a 15-inch macbook retina display, the pixels are separated by

$$d = \frac{15.6~\textrm{inch}}{\sqrt {2880^2+1800^2}} = \frac{0.396~\textrm{m}}{\sqrt {2880^2+1800^2}} = 1.17 \cdot 10^{-4}~\textrm m$$

From elementary geometry and optical path lengths (and small angle approximation), you can deduce that constructive interference occurs when there is an angle change from usual reflection of

$$\Delta \alpha = \lambda / d$$

If you hold the your laser at for example $b$ from the screen and your eyes are also at $b$ from the screen, the dots should appear to have a width

$$a = b \Delta \alpha / 2 = b \lambda / 2d$$

where the the factor of $\Delta \alpha/2$ came from the fact that the beam then has to reflect back at angle $-\Delta \alpha/2$ relative to normal to reach your eyes, so the difference is $\Delta \alpha$.

For $b = 0.5~\textrm m$ and $\lambda = 700~\textrm{nm}$, this gives $a = 1.5 ~\textrm{mm}.$

• @lswim: Could you please check whether the $1.5 mm$ displacement is the right order of magnitude for the diffraction dots, when both you and your laser are at approximately half meters from the screen (no need for measurements, just estimate). – kristjan Mar 2 '15 at 9:29
• That seems like a very plausible explanation (the displacement is certainly on the right order of magnitude) for the phenomena. I guess my one remaining question is, does the light not need to be coherent. I assumed the LED from a normal headlamp outputs incoherent light which would eliminate any interference patterns because all the waves would interfere differently. – lswim Mar 2 '15 at 9:33
• The time-averaged power emitted in different directions is the sum of the power by each wavelength (this can be shown with statistical mechanics). Thus in order to resolve the $n$-th maxima clearly, you need to have $n\Delta \lambda << \lambda$, which is usually satisfied by LEDs. You can see effects of diffraction also when you illuminate a CD with an extremely decoherent light, such an ordinary lamp or sun (just the wavelengths are separated) (see en.wikipedia.org/wiki/Diffraction_grating#mediaviewer/…). – kristjan Mar 2 '15 at 9:56
• for the sake of education, do you have a good deeper explanation of the coherence and resolving the n-th maxima. I hadn't heard that before and I'd love to learn more. – lswim Mar 2 '15 at 10:06
• @lswim Well, if $\Delta \lambda$ does not satisfy the above condition, then you can see that the $n$-th maxima starts to overlap with $n+1$-th maxima of another wavelength, making the nice diffraction pattern a rather smooth line. There is some information on the Wikipedia page (en.wikipedia.org/wiki/Diffraction#Coherence), but not very much. – kristjan Mar 2 '15 at 10:29