Phase and delay calculations in `DiscChopper.comp` disagree

[g5t]

The position in angle-space of a disc chopper in time is, e.g.,
$$\theta(t) = \omega t + \phi$$
where $\omega$ is the angular frequency and $\phi$ is the position of the disc at $t=0$, also known as the phase.

Equivalently, one can write
$$\theta(t) = \omega\left(t + \delta\right)$$
where the timing offset $\delta$ could be known as the delay.

It is therefore clear that we can relate $\phi$ and $\delta$ by
$$\phi = \omega\delta$$
or
$$\delta = \phi / \omega$$

Contrary to these relationships, the DiscChopper.comp definition treats calculation of $\phi$ from $\delta$ differently than the inverse:

McCode/mcstas-comps/optics/DiskChopper.comp

Lines 122 to 132 in 731e8ce

	/* Calulate delay from phase and vice versa */
	if (phase) {
	if (delay) {
	fprintf (stderr, "DiskChopper: %s WARNING: delay AND phase specified. Using phase setting\n", NAME_CURRENT_COMP);
	}
	phase *= DEG2RAD;
	/* 'Delay' should always be a delay, taking rotation direction into account: */
	delay = phase / fabs (omega);
	} else {
	phase = delay * omega; /* rad */
	}

There are two closed issues related to the DiscChopper phase, neither of which seems to directly relate to this problem:

1. DiskChopper, rotation seems to be left-handed with positive frequency #1128
2. DiskChopper: Phase is not calculated correctly from delay it seems... #377

Possible relevant supporting information is available in scippneutron's documentation

[g5t]

For concreteness, I believe the current calculation of phase = delay * omega; is correct, while delay = phase / fabs (omega); is incorrect.

[g5t]

There's a potential further definition issue. At least some control software for real-world disc choppers always calculate and set a positive delay time, $\delta \ge 0$, under the assumption that the disc position in time is

$$ \theta(t) = \omega \left(t - \delta\right) $$

This would then suggest

$$ \phi = - \omega \delta $$

and

$$ \delta = -\phi / \omega $$

➡️

 /* Calulate delay from phase and vice versa */ 
 if (phase) { 
   if (delay) { 
     fprintf (stderr, "DiskChopper: %s WARNING: delay AND phase specified. Using phase setting\n", NAME_CURRENT_COMP); 
   } 
   phase *= DEG2RAD; 
   /* 'Delay' should always be a delay, taking rotation direction into account: */ 
   delay = - phase / omega; 
 } else {
   phase = - delay * omega; /* rad */ 
 }
 if (delay < 0) {
 fprintf(stderr, "DiskChopper: %s ERROR: delay is a strictly positive quantity. Check your phase=%f or delay=%f input\n", NAME_CURRENT_COMP, phase, delay);
 }