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This article contains both beginner and more advanced content about the changing tilt of the sky. The technical word used to describe this is the parallactic angle, which is also encountered by astro-imagers who call it field rotation.
On April 3 2019 I walked out onto my backyard deck and immediately noticed the prominent halo around the Sun. Whenever the sky is not a clean blue I keep an eye out for halos, common and rare, caused by sunlight refracting through ice crystals: microscopic prisms spread the light into a spectrum of colours. For more details, consult the RASC Observer's Handbook and Les Cowley's atmospheric optics website (https://www.atoptics.co.uk/).
Halo displays can sometimes change on a 5-minute basis, yet at other times nothing really interesting happens over a period of several hours, challenging the patience of the dedicated halo-chaser. It's tough to have the luxury or discipline to step outside every 15 minutes to check. Even then one could miss out on seeing the dynamic changes. A reasonable compromise is to capture a time-lapse.
When imaging halos it is best to deal with the glare of the Sun and its inevitable lens flares. I had already created a rig to to block the Sun that attaches to the base of my camera: an occulting disk at the end of a telescoping arm (article and pictures). Better yet, I have the camera take a set of images at different exposures that I later combine to create an HDR image (High Dynamic Range), one that shows highlights close in to the Sun while simultaneously brightening any features that would otherwise be lost in the darker regions farther out. The following triplet of images shows the sky in the morning, near local noon, and late afternoon.
Because the average person doesn't look at the starry sky, they tend to miss its behaviour of rising up on a slant, crossing the south horizontally (transiting the meridian), then setting on a downward tilt:
The three panels show how Orion changes its tilt over the course of several hours (from a mid-latitude northern location). The white lines represent the RA and Dec grid we overlay on the sky for navigation.
An equatorial mount, following the central star of Orion's belt (Alnilam) rotates as it tracks, fixed on the grid, keeping Rigel (Orion's right foot) always at its lower right. In contrast, an AltAz keeps the camera upright relative to the ground while following Alnilam; Rigel will gradually move relative to Alnilam from the 4 o'clock position to almost 6 o'clock straight below. Imagers call this field rotation. Professional observatories working with AltAz scopes use a "field de-rotator" to turn the entire camera assembly slowly, matching the changing tilt and preventing the stars from trailing on the sensor.
Since keeping the Sun blocked is the most important part in capturing a halo sky, I set the StarAdventurer on solar rate in equatorial mode and let it run all day. When I attach the camera directly to the StarAdventurer, not using a ballhead, the long axis of the camera ends up exactly north-south by design. It's actually a disadvantage in this halo situation since the ground now rotates. More problematic is that complex halo displays are oriented vertically along the line from the Sun straight down to the ground. Without an AltAz mount, I actually need to de-rotate the sky!
For a much more complete article on field rotation, read Larry McNish's article https://calgary.rasc.ca/field_rotation.htm. As Larry notes, when you de-rotate after the fact, you lose the corners as can be seen here.
The StarAdventurer is designed to handle landscape time-lapses: the camera is slowly panned horizontally, so why not use that? The switches for sidereal, solar, and lunar tracking rates only work in equatorial mode. The problem is uneven speed: In horizontal mode (the bottom flat line), the mount tracks at a constant rate. But the Sun, in this exaggerated diagram, rises steeply and sets steeply, hardly shifting sideways. It only matches horizontal speed at the meridian. In my mid-latitude case it rises and sets on a diagonal, less of a mismatch, but enough that the camera and its occulting disk would not track the Sun.
De-rotation using the parallactic angle
De-rotation using the parallactic angle
Jean Meeus, in his wonderful book Astronomical Algorithms, has a formula for calculating the changing tilt:
tan q = sin H / [ (tan phi * cos delta ) - (sin delta * cos H)]
where H is the hour angle, phi is latitude, and delta is declination.
Next I run a perl program to loop through each image in my folder. In pseudo code:
foreach image.jpg do { extract image time using exifinfo module get H and declination of the Sun from Astro::Coord (given lat/lon/datetime) calculate q call imagemagick: convert image.jpg -rotate q output/image.jpg}Drop all the rotated images into a movie maker to get the final time-lapse:
There you have it, a practical application of handling field (de)rotation using the parallactic angle!
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