The shot is set up along alt-az lines - that works best near the horizon.

Here is how the mosaic panels are laid out, for a 200 mm focal length, full frame lens

4008As with the examples above, there are two grids - blue and red. Each one has very low overlap within the grid, but complete overlap between the two of them.

Each panel has edges which are great circles, so they are not rectangles. In the chart I approximate the great circles as polygons, but the calculations to line them up are correct. Altogether there are 84 panels in this mosaic.

This mosaic is for end of next week, when the bottom edge of the shot will be just above the horizon. The imaging quality is not great there but this is meant as the sky portion of a landscape astro shot, so I actually want the horizon effect.

Each panel has an associated orientation angle, so a field rotator will keep it in the proper orientation.

However the horizon imposes a problem - some of the subject will set below the horizon during the shot. This can be seen in the first chart above, where the horizon at various times is shown as the thin blue lines, which are spaced an hour apart.

To cope with the setting subject, the frames have to be shot in a priority order. That is shown by the Cyan colored lines, and the numbers.

]]>

This is counterintuitive so here is an explanation.

Here is a conventional 3 x 3 mosaic with 10% linear overlap - meaning that the horizontal frame overlap is 10% of the horizontal frame length, and vertical overlap is 10% of the vertical length. Of course our frames don't really look this when projected on the sky due to spherical trig, but it is a reasonable approximation for long focal length frames.

3942I am working on figuring out cases for wide field mosaics which then have substantial spherical impacts. More on that when I am done with it.

The x and y axes here refer to the panel size which is taken to be full frame (i.e. 36 x 24 units). Ultimately that turns into some angular coverage on the sky but we don't need to calculate that here.

There are 9 panels, and suppose we use 30 subs/panel. Then that is 270 subs.

The area covered is reduced a bit because of the overlap - it is (1+2*(1-overlap))^2 or 7.84 panels, treating a panel as having area = 1.

Here is an example of the new approach

3943This is 2 grids of 3 x 3 panels, each with zero overlap, but the two are shifted relative to each other, here by 10%.

Each panel now gets 15 subs - half of the conventional number.

The total panels is 18, so the total subs are 18*15 = 270 subs. The same as above! Yet each point within the "good" area of our picture (where the two grids overlap) still has 30 subs.

The area of the good area is slightly larger than the conventional case, it is (3 - overlap)^2 = 8.41.

In order to compare the relative efficiency, we need a metric

A reasonable metric is (total subs count)/(subs coverage *good area). Of course one could invent a better metric, but this corrects for the fact that the good areas are slightly different.

The conventional case is 270/(30*7.84) = 1.15, while the new case is 270/(30*8.41) = 1.07.

Roughly speaking what this tell us is the "sub efficiency" of a mosaic plan. I should expect to waste roughly 15% of the subs due to mosaic overlap in the conventional scheme with 10% linear overlap. I only waste 7% in the new scheme.

That difference is pretty small, but it turns out that the advantage of the new method grows with the size of the mosaic

3944This is a simple analysis that only counts N x N mosaics, where N is the x-axis in the plot. I have plotted the conventional case for overlap = 10%, 20%, 30%

In the new approach there is little reason to vary the shift between the 2 grids so I have left it at 10%.

The metric shows us that as N becomes large the metric tends to 1 for the new scheme. At N=10, it is 1.02. That is because the only wastage in this approach are the narrow strips where the grids do not overlap.

Meanwhile for N=10, the conventional approach with 10% overlap is 1.42.

10 frames overlapped by 10%, creates a grid that is 8.4 frame units long. The overlap compounds with N.

If we were doing 100 panel mosaics (which I am gearing up to do), then the conventional method with 10% overlap would require 4260 subs, while the new method would take 3060, so it would save roughly 28% of the time to do the new method.

One could say that the new method requires too much accuracy because I am assuming that one can have the frames touch each other. I think that is actually quite reasonable if you do a plate solve for each position - the accuracy can be within a very small fraction of the frame size (10s of pixels).

]]>

Recall that for stars the f-stop does not matter - the light gathering power depends on the area of the aperture. So a 50 mm f/2 lens and a 100mm f/2 lens both are f/2, but for stars the 100mm lens has 4X the light gathering power.

Plus, it is harder to have good edges with wide angle designs. I could not find a wide angle lens that had good stars at the edge wide open. When you start stopping down the lens you strangle the light gathering.

A 24mm f/1.4 lens has terrible edges at f/1.4. Most of the need to go to f/4, at which point its aperture is

Cropping the 24mm images does work - but it is not competitive with a decent 50mm lens stopped down until

Meanwhile a 135mm Samyang/Rokinon f/2 (or Zeiss for more money) is good to the edges wide open at f/2.

The 135mm at f/2 has 126X the light gathering power of the 24mm at f/4. So you need to take more images to cover the same field but you get a better result.

]]>

With a single image that is often OK because the subject is in the center.

With a mosaic, we take our image edges and put them into the subject area. That's potentially a problem, *regardless* of what overlap scheme you use.

As you point out, there are fixes for the edge problems, which remove the vignetting. Many people crop off the ragged edge of the panels where guiding has made overlap imperfect.

But I view these as different problems that are largely unrelated to SNR, because SNR does not fix them. If the edges of your frame have stars that are not round due to coma, no amount of stacking more copies of bad edge stars on top is going to help.

In minimum overlap (i.e. 10% overlap) mosaics, you are stacking N copies of the extreme right edge of one frame with N copies of the extreme left edge of the next frame. The outermost 10% of the frames is going to be the worst. While coma can be directional, it's not usually the case that two wrongs make a right. So the places where edges are stacked are going to look bad. The overall mosaic will have regions that are good (center-stacked-on-center) and strips which are bad (edges-stacked on edges).

In maximum overlap mosaics - which is the approach I am exploring - where you overlap by 50% - that tends to average together the edges and the centers. So if your edges are bad, this will effect the whole image, but I believe it would be more uniform.

I think that the lesson here is: don't have bad edges! If you have poor optical quality at the edge of frame, your mosaic will suffer. So you need to either get a different optical system, or stop the lens down, or crop off the bad portion off of the frames.

]]>