Whilst we could prove these using the unit circle or the graphs of our trigonometric functions, it is enough to simply quote the CAST diagram. We can therefore conclude that sin 𝑥 is greater than zero in the first and second quadrants. When the angle 𝑥 lies between zero and 180 degre...
sin(θi)+sin(θo)=mλ/nΛ Eq. 1 where Eq. 1 is diffraction (or reflection or scatter) relationship between input wavelength λ, input incident angle θi, output incident angle θo, and the spatial period Λ of the grating 12. Further, m is the “order” of the reflection ...
sin(θi)+sin(θo)=mλ/Λ Eq. 1 where Eq. 0.1 is the diffraction (or reflection or scatter) relationship between the input wavelength λ (in free space or vacuum), input incident angle θi, output incident angle θo, and the spatial period Λ of the grating 12. Further, m...
This is a useful and general method for calculating the mean phase. The circular mean of a set of angles (ai, i = 1…n) is defined as 𝑎𝑚=arg(𝑋,𝑌) 𝑤𝑖𝑡ℎ 𝑋=∑𝑖=1𝑛cos(𝑎𝑖) and 𝑌=∑𝑖=1𝑛sin(𝑎𝑖)am=arg(X,Y) with X=∑i=1ncos(ai...
𝛽(𝜑,𝜃,DOY)=𝛿1+𝛿2𝜑+𝛿3𝜃+𝛿4cos(2𝜋DOY365.25)+𝛿5sin(2𝜋DOY365.25)+𝛿6cos(4𝜋DOY365.25)+𝛿7sin(4𝜋DOY365.25),β(φ,θ,DOY)=δ1+δ2φ+δ3θ+δ4cos2πDOY365.25+δ5sin2πDOY365.25+δ6cos4πDOY365.25+δ7sin4πDOY365.25, (4) where 𝜑φ,...
[𝑉𝑈𝑉𝐻]=⎡⎣⎢cos𝜃𝐴scos𝜃𝐷𝑒−sin𝜃𝐴scos(𝛽−𝛼𝐴s+3𝜋2)−sin𝜃𝐷𝑒cos(𝛽−𝛼𝐷𝑒+3𝜋2)⎤⎦⎥−1⋅[𝑉𝐴𝑠𝑉𝐷𝑒]VUVH=cosθAs−sinθAscos(β−αAs+3π2)cosθDe−sinθDecos(β−αDe+3π2)−1⋅...