spot array generates non-uniform pitch spot arrays about slmsuite HOT 4 CLOSED

Hmm. I think this is actually intended behavior. Looks like integer rounding to me, where the upper spots happened to be rounded up one in the (integer) computational k-space knm.

Internally, a grid is created in .make_rectangular_array() from x and y lists on each edge:

x_edge = (np.arange(array_shape[0]) - (array_shape[0] - 1) / 2)
x_edge = x_edge * array_pitch[0] + array_center[0]
y_edge = (np.arange(array_shape[1]) - (array_shape[1] - 1) / 2)
y_edge = y_edge * array_pitch[1] + array_center[1]

But then, the points generated from these edges are ceiled up.

self.spot_knm_rounded = np.ceil(shape / 2 + self.spot_knm.astype(np.float))
self.spot_knm_rounded = self.spot_knm_rounded.astype(np.int)

The fix is either to increase the resolution of k-space to be finer (and the off-by-one less noticeable), or choose array_shape and array_center more carefully to avoid undesirable rounding.

Rounding is going to happen no matter what, which is why this is intended behavior. I added a user info note in 7a84c9c.

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I realized this would affect results of fourier calibration so I spent some more time thinking about it. I am proposing that we adopt the convention I declared here:

The x_edge and y_edge computation is fine because the results are floats with uniform pitch. I think spot_knm_rounded is funky due to the ceil. For example, say shape / 2 + self.spot_knm.astype(np.float)) has x coords 58.6, 64, 69.4: 58.6 is rounded up to 57, 64 stays, 69.4 is rounded up to 70, so the array isn't uniform anymore. You can prove by considering a few simple cases that, under the convention I proposed, two points equally spaced about zero (58.6 ~ -5.4) and (69.4 ~ 5.4) always end up an equal number of indices away from zero.

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The ceil was intended to make the rounding explicit. The rounding has to occur no matter what, to generate a target image in computational k-space. I'm not sure if the proposed convention resolves the problem, as you're back to non-uniform pitch once you do more than three points in the example (e.g. five points). The heart of the issue was passing a non-integer knm pitch in the first place, I would argue, which is a user issue that we can (at best) warn about.

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But after some discussion, around probably produces better results than ceil in the case of spot_knm_rounded, as this more accurately targets the positions of desired spots. See 2a958cc.

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