`shift_x_y_to_zk1_2_wavediff()` function has dimensional inconsistencies

[jeipollack]

Hi @tobias-liaudat,

There seems to be a dimensional analysis issue in the code you originally wrote. Since you're most familiar with the intended physics here, could you take a look?

In the code snippet below, the function takes arctan() of a quantity with units [1/m], which is dimensionally incorrect:

wf-psf/src/wf_psf/utils/preprocessing.py

Lines 39 to 44 in 7c4b515

	return (
	zernike_norm_factor
	* (tel_diameter / 2)
	* np.sin(np.arctan((dxy / reference_pix_sampling) / tel_focal_length))
	* 3.0
	)

Moreover, this function is called incompute_zernike_tip_tilt. There, the arg passed in is the displacement pixel shift multiplied by pixel_sampling=12e-6 m, which will do the conversion from the [pixel] units to [m].

wf-psf/src/wf_psf/utils/centroids.py

Line 87 in 7c4b515

zk1_2_array = shift_x_y_to_zk1_2_wavediff(displacements_swapped.flatten() * pixel_sampling ) # vectorized call

But, then this is undone by division by reference_pix_sampling = 12e-6 in shift_x_y_to_zk1_2_wavediff in the arctan function above. Both values are the same, making this conversion roundtrip unnecessary.

Just to add: this pattern also appears in the original code from last year:

   current_shifts = centroid_calc.return_shifts()  # In [pixel]

    dx = reference_shifts[1] - current_shifts[1]  # In [pixel]
    dy = reference_shifts[0] - current_shifts[0]  # In [pixel]

    z1_wavediff = shift_x_y_to_zk1_2_wavediff(dx * pixel_sampling)  # Input in [m]
    z2_wavediff = shift_x_y_to_zk1_2_wavediff(dy * pixel_sampling)  # Input in [m]

    return (
        z1_wavediff,
        z2_wavediff,
    )  # Output in Zernike coefficients in wavediff convention

Could you help clarify the intended physics and suggest how to make this dimensionally consistent? I can think of a couple of approaches, but you're the expert and so I'd value your input. Thanks!