Monday, April 14, 2014

Moon Photography: Stellarium, Focal Length, and Exposure Times.

On Apr. 15, there will be a total lunar eclipse visible from almost the entire North American continent. The next total lunar eclipse visible from the east coast will not be until 2015, and the next total lunar eclipse visible from the entire North American continent will not be until 2019, so this is a rare opportunity to get some really unusual photographs.

Here is the field of view one can expect from a few common configurations:

D800E @ 200mm with 2X TC
D7000 @ 200mm with 2X TC
D7000 @ 200mm
D800E @ 200mm
D7000 @ 50mm
D800E @ 50mm

How to make simulations like these for any camera:

(Or skip to exposure time section)

Stellarium is an open source planetarium software that is capable of simulating the sky and celestial bodies at any time as seen anywhere on earth (and from most other known planets and moons). It's a good way to know exactly when and where you should be looking based on your exact location. If you are photographing through a telescope, it also can drive many telescopes to track the moon and other celestial objects.

General Stellarium Setup

Location selection is the top option on the leftmost menu. You can search for a city or enter precise GPS coordinates if you have them, or just click around the map.

The second option on the left toolbar is the date and time, which you should set to about 1:00 on April 15th. On the right side of the bottom toolbar the fastforward, rewind, normal, and current time buttons allow you to travel back and forth in time through the entire event.

Once you have the location, date, and time selected, Stellarium will be displaying a view of the night sky that allows you to zoom and pan around and click on celestial bodies for information.

Camera and Lens Simulation (Oculars plugin) 

However, we're interested in simulating the view through a specific lens onto a specific camera sensor. To do that, we want to use the Oculars plugin. Oculars may be enabled automatically, but if it isn't, it can be enabled under Configuration Window > Plugins > Oculars. Be sure that the "Load at startup" option is selected.

The Oculars configuration window is where you can specify a camera and lens combination. Here's an overview of the important parts of the settings panel:

General As far as this guide is concerned, check all three boxes on top and enable the on-screen interface.
EyepiecesThis is where eyepiece information is specified; it can be ignored for astrophotography because we are targeting a sensor as the final element.
LensesThis is where you should specify a teleconverter, if applicable, not the lens you are using.
SensorsThis accepts information about the exact sensor you're using. Stellarium uses this sensor information to calculate crop factor and other information, but for a quick-and-dirty view, the pixel seze can be omitted (just put in 4.8).
TelescopesThis is where information about your lens goes. Diameter can be omitted (set to 80) if you just want a field of view estimate.
AboutThis one explains itself. That's the point.

Now you should have four buttons in the upper right corner: telescope view, sensor view, scope view, and settings. Selecting sensor view (the rectangle) draws the red rectangle on the screen and opens up a menu where you can select the camera and lens setup you entered earlier. For example, the image on the left shows the simulated view of the setup I plan on using on the 15th.

Exposure Time

Again, I'll offer a cheat-sheet before my derivation:

Nikon D700, APS-C 16.2 mp, with no motion blur:
200mm lens: 1/4s or faster
400mm lens: 1/6s or faster
1250mm lens: 1/20s or faster

Nikon D7100, APS-C 24.1 mp, with no motion blur:
200mm lens: 1/4s or faster
400mm lens: 1/8s or faster
1250mm lens: 1/25s or faster

Nikon D800E, Full frame 36.3 mp, with no motion blur:
200mm lens: 1/4s or faster
400mm lens: 1/8s or faster
1250mm lens: 1/25s or faster

The D7100 and D800E have the same speeds because even though the D800 has more resolution, its pixels are spread out over a wider area then the D7100, and it just happens to round out roughly equal.

In general astrophotography, some people use the "Rule of 600" to estimate how long of an exposure time we can use before the stars start to visibly exhibit motion blur. It states that 600 divided by the 35mm equivalent of the focal length of the lens gives the exposure time in seconds of an acceptably sharp image. For example, the 200mm lens with a 200mm teleconverter on my D7000 is 600mm equivalent, and 600 / 600 = 1, so 1 second is approximately the longest amount of time I should expose the stars. That 400mm lens on my APS-C camera has an angle of view of about 3.34° (2arctan((35)/(2*(1.5*400)))), projected onto 4,928 horizontal pixels, so each degree of view is projected over 1,475 pixels. Therefore, assuming the worst-case scenario is that the fastest stars will appear to move at 0.0042 arc minutes per second (360° over 24 hours), 1 second is 0.0042' of movement, which equals a blur of 6.1 px.

The moon moves 13° more per night then the background stars, so it would have 6.3 pixels of motion blur with the same lens and one second exposure. Because the moon is the entire focus of the image, I think 6.3 px is way too much blur. To reduce the moon-motion blur to three pixels, we would need to expose for no more than 1/2 second, and to remove motion blur entirely, no more than 1/6 seconds.

This means that acceptable exposure times go down drastically with the length of the lens; my 1250mm telescope will have three pixels or more of motion blur at 1/6 second, and it will have to be faster than 1/20s in order to actually freeze the moon.

Keep in mind that my D7000 does not have an incredibly high resolution sensor, and to freeze motion on a higher resolution camera would require faster speeds. The D7100 has 24.1 mp across the same image sensor area, so through the 400mm lens it would require a shutter speed of 1/8 to fully freeze the moon, or 1/25 through the telescope. Achieving proper exposure with these shutter speeds isn't an issue with a brightly lit moon, but when it passes into the sun's shadow these limits may come into play.

Keep in mind that taking photos at faster shutter speeds than these will not improve sharpness, (assuming that the camera is on a tripod and triggered by a remote shutter) so it's better to use these speeds with as low of an ISO as possible instead of boosting ISO to increase shutter speed.