Alt-Az Field Rotation Exposure Calculator
Enter your latitude, target position, camera frame size, and blur tolerance to estimate the maximum sub-exposure before alt-az field rotation smears the sensor corner.
Maximum rotation-limited exposure (seconds)6.57
- Conservative whole-second exposure
- 6
- Current field rotation rate (degrees/minute)
- 0.29
- Planned-exposure corner blur (pixels)
- 4.57
- Planned exposure assessment
- Over limit: predicted corner blur is 4.57x the allowed blur.
- Sensor corner radius (pixels)
- 1,802.78
Uses the instantaneous field-rotation rate at the entered altitude and azimuth.
Assumes the tracked target is centered in the image and checks blur at the farthest sensor corner.
How to use this calculator
- Enter the observing latitude, using negative values south of the equator.
- Enter the target altitude and azimuth for the time you plan to expose.
- Enter the saved image dimensions after any binning or crop.
- Set the corner-blur tolerance and planned exposure, then compare the limit with your sub length.
How the field-rotation exposure is calculated
An alt-azimuth mount can track a target's altitude and azimuth, but the camera frame still rotates against the sky unless a derotator or equatorial platform removes that motion. This calculator uses the instantaneous field-rotation relation for an alt-az mount, then converts that angular rate into pixel motion at the farthest corner of the saved image.
The rotation rate is computed as:
Rdeg = (360 ÷ 86164.0905) × cos(phi) × cos(A) ÷ cos(h)
- phi is observer latitude.
- A is azimuth measured clockwise from north.
- h is target altitude above the horizon.
- Rdeg is degrees per second before taking the absolute value.
The sidereal day constant, 86164.0905 seconds, converts Earth's rotation to sidereal degrees per second. The calculator converts the absolute rate to radians per second, finds the sensor-corner radius with r = sqrt(W^2 + H^2) ÷ 2, and uses the exact endpoint chord for a rotated point:
b(t) = 2r × sin(Rt ÷ 2)
Solving that equation backward for an allowed corner blur B gives the exposure limit:
tmax = 2 × asin(min(1, B ÷ (2r))) ÷ R
For normal short sub-exposures the small-angle version, b ≈ rRt, gives nearly the same answer.
What moves the result most
The altitude and azimuth usually matter more than the camera dimensions. Rotation becomes severe near the zenith because the formula divides by cos(h). North or south targets can have a larger instantaneous rate, while east and west azimuths are zero crossings where the instantaneous rate can vanish. A larger saved frame also lowers the limit because the farthest corner is farther from the rotation center.
What this calculator leaves out
The result is an instantaneous limit at the entered sky position. The rate changes during an imaging session, especially near the zenith and near east-west zero crossings, so a long sequence should be checked at several times. The model assumes the tracked target is centered on the image. It estimates only field-rotation blur and excludes tracking error, wind, seeing, focus drift, atmospheric refraction, optical aberrations, stacking-edge loss, and any derotator behavior.
Worked example
At latitude 35° with a target at 45° altitude and 180° azimuth, the field-rotation rate is about 0.29 degrees per minute. A 3000 by 2000 pixel image has a corner radius of sqrt(3000^2 + 2000^2) ÷ 2 = 1802.78 pixels.
With a 1 pixel corner-blur limit, the reversed chord equation gives a maximum exposure of about 6.57 seconds, so the conservative whole-second setting is 6 seconds. A planned 30 second exposure predicts about 4.57 pixels of corner blur, which is about 4.57 times the allowed blur.
Common questions
Why does field rotation become extreme near the zenith?
Near the zenith, a small movement of the sky can require a rapid change in azimuth. The field-rotation formula divides by cos(altitude), and that value approaches zero as altitude approaches 90 degrees. That is why an alt-az exposure limit can collapse even when tracking looks accurate at lower altitudes.
Why are focal length and pixel size not required?
This calculator works in saved image pixels. Once you choose an allowed blur in pixels and provide the image width and height, the field-rotation smear at the corner depends on the rotation angle and pixel radius from the center. Focal length and pixel size matter for other image-quality limits, but they are not needed for this pixel-coordinate rotation check.
Where do I find my target altitude and azimuth?
Most planetarium apps and telescope-control programs show current altitude and azimuth for the selected target. Use the values for the middle of the exposure or for the part of the session where you want the most conservative check. Recheck later if the target is moving toward the zenith.
Does GoTo tracking eliminate field rotation?
GoTo tracking on an alt-az mount keeps the target centered by driving altitude and azimuth axes. It does not rotate the camera to follow the parallactic angle, so the field can still rotate around the tracked point. A mechanical field derotator or a properly polar-aligned equatorial setup changes the problem.
Should blur be checked at the sensor corner or edge midpoint?
The corner is the conservative place to check because it is farthest from the rotation center when the target is centered. An edge midpoint has a smaller radius and therefore less field-rotation blur. If you crop heavily around the center, enter the cropped saved dimensions rather than the full sensor dimensions.
Why can the calculated limit change during an imaging session?
Altitude and azimuth change continuously as Earth rotates, and the field-rotation rate depends directly on both. The instantaneous zero at east or west does not mean a long exposure or a long sequence has zero rotation. For critical work, calculate the limit for several times across the planned session.