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My thinking is that each slit is a Huygens source, radiating cylindrical waves homogeneously in every direction, but due to interference, only those with constructive interference can exist. I guess the energy going into each order should be equal, which is not the case. So I am confused on how the light will distribute its energy to different orders. Thank you.
Imagine a grating with infinite number of slits, and the spacing D between slits is larger than the wavelength so that there are high order diffractions. In each of the diffraction directions the waves constructively interfere, but what decides the percentage of power that goes into each order?
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There are two steps only you need to calculate the intensity distribution behind a multi slit. Firstly you have to calculate the intensity distribution pattern behind a single slit. Secondly you has to calculate the aberration of the pointlike source to all the slits and to the observers screen and by this sumerize the intensities at all interesting you points.
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$$ \delta(x) \quad \overset{\mathcal{F}}{\underset{\text{(far field)}}{\Longrightarrow}} \quad 1 \cdot g(x) \quad \overset{\mathcal{F}}{\underset{\text{(far field)}}{\Longrightarrow}} \quad \text{sinc}(\pi D_1 x) \cdot \delta_{1/D}(x) $$
$$ \text{light source} \quad \overset{\mathcal{F}}{\underset{\text{(far field)}}{\Longrightarrow}} \quad \text{grating} \quad \overset{\mathcal{F}}{\underset{\text{(far field)}}{\Longrightarrow}} \quad \text{observation screen} $$
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So the energy depends on the fill-factor $D_1/D$ of your grating. The larger $D_1/D$, more energy at $0^{\text{th}}$-order.
Laser pointers, considered a class 3A laser, are battery-powered handheld device that emits visible laser light that is created for variety of uses from pointing out objects or locations to being pet toys. They can come in various designs and sizes emitting different colors at varying powers.
We identify the intensity be $|\text{sinc}(\pi D_1 x)|^2 \cdot \delta_{1/D}(x)$, i.e. discretized $|\text{sinc}(\pi D_1 x)|^2$ sampled at $D$ period, which is also known as the diffraction orders.
The blink reflex, also called aversion response, is effective enough to protect the eye from any potential laser damage with lasers that have an output power less than 5 milliwatt (mW).
Let a single slit be $a(x)$, and denote $\delta_D(x)$ as the Dirac comb of spacing $D$. Denote $\star$ as convolution, the grating is: