Retardance above pi

[gschlafly]

Need to check if calculation and interpretation is appropriate

[pvjosue]

High retardance that goes over 2*pi

[gschlafly]

Retardance is high for a shell with pytorch and numpy backends.

[gschlafly]

Adjusted the creation of the ellipsoid/shell so that the birefringence values were not overwritten by the mask:
vol[0,...] = vol[0,...] * combined_mask.astype(float)

However, the retardance still should not be able to go above $\pi$ even with a highly birefringent object.

[gschlafly]

The retardance function should only output values between $0$ and $\pi$:
https://github.com/PolarizedLightFieldMicroscopy/GeoBirT/blob/ac9075d681375ebd2d64a9635217e086eeca5dd7/src/VolumeRaytraceLFM/jones/eigenanalysis.py#L65-L68
Thus, the angle calculation should only output values between $0$ and $\pi/2$:
https://github.com/PolarizedLightFieldMicroscopy/GeoBirT/blob/ac9075d681375ebd2d64a9635217e086eeca5dd7/src/VolumeRaytraceLFM/jones/eigenanalysis.py#L5-L21
Consequently, the real part of $a$ should be nonnegative.

To Do

• Figure out what causes the real part of $a$ to be negative.

[gschlafly]

The real part of the first element of the jones matrix, $a$, is the cosine of the accumulated retardance. The retardance is positive. So the negative real component of $a$ is introduced from the product of the jones matrices.

[gschlafly]

The phase wrapping effect should be accounted for in the final step of calculating the retardance from a jones matrix.

# Calculate the phase differences (retardance)
retardance = np.angle(eigenvalues[0]) - np.angle(eigenvalues[1])

# Normalize the phase difference to [0, 2*pi) and assure values are positive
retardance = (retardance + 2 * np.pi) % (2 * np.pi)

# Wrap the phase difference to [0, pi]
if retardance > np.pi:
    retardance = 2 * np.pi - retardance