How to Plot Polar Scalar Fields

Question

I am trying to plot the following two equations (where $k_y=k\sin(\theta)$):

$$F(k_y,k_z)=e^{-ika\sin(\theta)}+e^{ika\sin(\theta)}$$ $$F(k_y,k_z)=e^{-ika\sin(\theta)}+e^{ika\sin(\theta)}+e^{-ika\sqrt{2}\sin(\theta)}+e^{ika\sqrt{2}\sin(\theta)}+2$$

I've tried rewriting them as the following, but it hasn't helped me figure it out:

$$F(k_y,k_z)=2\cos(ka\sin(\theta))$$ $$F(k_y,k_z)=2\cos(ka\sin(\theta))+2\cos(ka\sqrt{2}\sin(\theta))+2$$

They are scalar fields, but in terms of polar coordinates. How would I go about plotting these?

(If it's helpful - these are the equations I have come up with for two separate 2-D diffraction patterns.)

Answer 1

As written this is not really a field but a contour which can be plotted as follows:

ka = 10
f[theta_] := 2*Cos[ka*Sin[theta]] + 2*Cos[ka*Sqrt[2]*Sin[theta]] + 2
PolarPlot[f[x], {x, 0, 2 Pi}]