Virgo Cluster Mosaic Ib: A Less Aggressive Approach

Last time I settled on using a 200mm lens to make a mosaic of the entire--fifteen degree square--Virgo Cluster. This would require something on the order of 15 to 24 subimages.

A club member pointed out that the galaxies probably wouldn't look very good at that scale, and he was right. Here's a simulation of 200mm vs. 700mm.

700mm image

200mm simulation

The galaxies are starting to lose their distinction from stars, pretty much ruining the point of a galaxy cluster mosaic.

His solution is to image only the core of the cluster, an area of about 8° by 5°. That's roughly 1/5 of the entire cluster's expanse, but it does contain the densest concentration of galaxies of interest to visual observers.

I'm going to repeat the calculations from Part I for the AT65 telescope. N = 3.5 (round up to 4) and M = 3.25 (round up to 4). So this can be done with about 16 images using much better optics.

I had some time to put together the layout of the 16 frames:

Virgo Cluster mosaic layout. Blue box, suggested area to be imaged; green markers, centers of subframes; red marker, center of mosaic; red box, area of mosaic.

The final mosaic will have a pixel counts that are about three times the frame dimensions. Since I'll be using a Canon T2i, that will give a 162 megapixel mosaic!

Virgo Cluster Mosaic I: Choosing a focal length

The galaxy imaging I did this spring was so much fun that I'm considering a big project: A mosaic of the Virgo Cluster. One of  the club's members suggested that such a project could result in a poster that would be suitable for fund raising at the 2018 Astronomical League Convention (which the club is hosting). I don't know anything about poster printing and marketing, so I'll leave that to others.

The mosaic, on the other hand, interests me.

My images were all taken using my TV-102; with the 0.8X FF/FR it has a focal length of 700mm and a field of view using an APS-C DSLR of about 1.3° by 1.1°. That's too small a field to make this practical--The Cluster has a size of about 15° by 15°, which is an area about 140 times the TV-102 field. When overlapping is considered it gets even more impractical. I would like to finish this within my lifetime!

Another option is my AT65 (422mm FL) with a field that's 3° by 2°. This means I'd need 38 images not counting the area lost to overlap needed for proper alignment. This is better, but still quite a task, and nearly impossible given the fickle weather around here.

How about a 200mm lens? Its field is 5.1° by 3.9° and gives about 12 images needed before overlap is figured in. That's not bad. A big galaxy like M84 manages to be about 85x74 pixels, also acceptable. It's time to pin down the cost of overlapping.

Consider a single line made of identical overlapping images. We take W as the image width and A as the overlap between one image and the next.

The width of sky covered by the first image in the line is W. Each additional image in the line adds (W - A) to the line length, making it easy to write an expression for the total line width W:

W =W + (N-1)(W-A)

We can solve this for N:

N = (W - W)/(W-A) + 1

Pretty simple, huh? We can do the same for height, letting M equal the number of images of height H in a column, B be the overlap distance, and H the total height of the column.

M = (H - H)/(H-B) + 1

We can fiddle with this a little more to express the overlap as f, the fraction it is of the width or height. This is useful because we'll almost certainly try to use the same fractional overlap in both directions.

f = A / W = B / H

N = (W - W)/[W(1-f)] + 1
M = (H - H)/[H(1-f)] + 1

One more change, let's define the constant F equal to 1/(1-f), giving
N = F(W/W - 1) + 1
M = F(H/H - 1) + 1

Notice that the right hand side of these expressions doesn't necessarily guarantee that N and M are whole numbers. It's up to us to round them up or down to an integer value depending on how well the resulting grid of subframes covers the target area.

One more alteration improves the convenience:

N = F(W/W - 1) + 1
M = F(H/H - 1) + 1

We should check this pair of equations for correct behavior in the case of no overlap. In that case f = 0 is zero and F = 1. This gives 

N = (W/W - 1 + 1 = W/W
M = (H/H - 1 + 1 = H/H

The number of subframes, N times M, is equal to (WH) / (WH), the area of the mosaic divided by the area of a subframe. This is exactly right in the limit that the subframe is much smaller than the mosaic and we can ignore the need for N and M to be whole numbers.

For the 200mm lens, we have (expressing everything in degrees) W = 5.1 and H = 3.9. For the Virgo Cluster both H and W are 15, so

N = F(1.94) + 1
M = F(2.84) + 1

Let's assume a 1/3 overlap rule, so F = 1 / (1 - 0.333) = 1.5.  This gives us

N = 1.5(1.94) + 1 =  3.91 (round up to 4)
M = 1.5(2.84) + 1 = 5.26 (round up to 6)

So--as a first guess--24 images are needed to make a rectangular mosaic of the Virgo Cluster.This could be as few as 15 (3x5), 18 (3x6), or 20 (4x5) depending on the fit and composition considerations. I'll leave that for Part II.

How about a 135mm lens that gives a 9.5° by 6.3° field?

N = 1.5(0.58) + 1 =   1.87 (round up to 2)
M = 1.5(1.38) + 1 =   4.47 (round up to 5)

Only 10 images, but the galaxies would be awfully small.

And for my AT65, with a a 3.0° by 2.0° field?

N = 1.5(4.0) + 1 =   7
M = 1.5(6.5) + 1 =   10.75 (round up to 11)

77 images, a bit much for my taste, and really difficult to get done by ALCON 2018.

Just for fun, let's do the case for the TV-102.

N = 1.5(0.58) + 1 =   16.8 (round up to 17)
M = 1.5(2.38) + 1 =   19.95 (round up to 20)

That's a mosaic with 340 subimages. That's not going to happen.

Markarian's Chain

The Minnesota Astronomical Society (MAS) has sponsored Messier Marathons for many years. Recently they've begun holding the marathon twice a year by adding a fall gathering for what's called the mini-marathon.

The spring marathon gives everyone a long, good look at the Virgo cluster of galaxies, home to 16 Messier Objects. There are more than just Messier galaxies in the cluster and deciding which particular faint fuzzy you see in your eyepiece can be difficult. Navigating the Virgo cluster is difficult for anyone who hasn't done it frequently.

Beginners wander into the cluster not just during marathons but also when working on their Messier lists. It's not unusual for them to leave the cluster with a sense of frustration.

With that frustration in mind the MAS started what it calls the Virgo Venture, a spring evening during which all attention is on the cluster and learning how to navigate it. Special star-hopping charts are provided and there's an experienced navigator around to help observers find their way.

It was at one of these Ventures that I first observed Markarian's Chain, a gentle arc of galaxies in a small patch of sky. It was the first time that I'd seen more than two galaxies in the same field of view. In fact, I could count six, and with a little travel add a few more! I was impressed, and it marked a first appreciation of wide field viewing for me.

This year's Venture was held last Saturday despite thinning cirrus clouds running east-west over the site and a thick plume of smoke from Canadian wildfires. My imaging target was the Chain but given the overhead murk I didn't have a lot of hope. I shot an hour of light frames with the haze and another hour as the haze was disappearing, so it didn't turn out too badly.

The entire group of galaxies fits tightly in the 700mm view of a TV-102 with its focal reducer/flattener in place:

Markarian's Chain, stretching from the two fuzzies in the upper left corner to M84 near the right edge.

The acquisition details are at AstroBin. Briefly this is two hours of light frames using a modified Canon T2i at ISO 800, a TV-102 at f/7, and autoguiding.

The weather forecast suggests a week of clouds and then the moon comes back. A good cycle to do some lunar/planetary imaging, I suppose. June's new moon will bring a last shot at many Arp galaxies, and then it's summer and back to nebulae!

M81 and 82 Revisited

A nice clear night and an opportunity to image from a friend's home north of the city lights produces a pretty picture:

 

This is based on 44 x 3m light frames with 15 dark frames, Canon T2i at ISO 800 on a TV-102 at f/7.

Power saving update: the software I talked about that turned off the laptop LCD display wouldn't keep it off. Apparently something about using ImagePlus kept turning the display back on. This wouldn't be a problem if a hand control was used to run the DSLR and images were stored on-camera.

Battery Update: I ran the laptop (fully charged), dew prevention, mount and camera from the 35Ah battery for four hours; loaded voltage fell from 12.7 (unloaded, 13V)  to 11.8V. Unfortunately I popped the battery onto the charger as soon as I got home and didn't check its final unloaded voltage.

Assuming it was 12.1V it would have been at 50% capacity, meaning it would have supplied about 17Ah or about 4Ah per hour. This is about right if I take into account that the old laptop battery was in place and it could run the laptop for maybe two hours, after which the 35Ah battery was supplying 6A to both run the laptop and recharge its battery.

That's a whole lot of assumptions and guesses, though, so it doesn't mean much. I may end up rewiring the battery box to include an ammeter so that I can monitor power use more rigorously.