The GSD can be calculated using the geometry of the imaging setup.
General case (oblique or slant view) In the general case where the sensor may be imaging the ground at an oblique angle (i.e., not
looking directly down), the GSD is given by: \mathrm{GSD} = \frac{R_S \times p}{f \times \cos(\theta)} Where: • \mathrm{GSD} is the ground sample distance, e.g., in cm/px; • R_S = \sqrt{d^2 + h^2} is the
slant range from the sensor to the point on the ground, e.g., in meters: • d is the horizontal distance (or offset) from
nadir, e.g., in meters; • h is the
height above ground level (AGL) of the sensor, e.g., in meters. • p = P \div N is the physical pixel size of the sensor, e.g., in micrometers: • P is the physical
width or height of the sensor, e.g., in millimeters; • N is the
number of total pixels in the same dimension as P. • f is the
focal length of the camera lens, e.g., in millimeters; • \theta = \arctan \left( d \div h \right) is the slant angle from nadir (which would correspond to 0°), e.g., in degrees. The cosine of \theta accounts for the oblique viewing angle, which increases the effective ground footprint of each pixel.
Nadir case (look-down view) In the special case of a
nadir view, i.e., when the sensor is looking directly downward, the formula is simplified since d = 0. Thus, R_S = h and \theta = 0, the cosine of which is 1. Therefore, the formula becomes: \mathrm{GSD} = \frac{h \times p}{f} Where all variables are defined as above.
Planar components derivative formula If the slant range R_S and slant angle \theta are to be derived from the
horizontal and vertical components d and h thereof, after simplification, the formula becomes: \mathrm{GSD} = \frac{d^2+h^2}{h} \times \frac{p}{f} Where all variables are defined as above.
Optimal off-nadir angle for maximal distance To maximize the horizontal imaging distance (d) for a given optical system while adhering to a specified maximum ground sample distance (\mathrm{GSD_{max}}) constraint, the optimal imaging geometry is achieved at a 45° off-nadir angle. This corresponds to a height above ground level (h) equal to the horizontal distance between the target point (d) and the sensor. This configuration is useful for planning aerial or satellite imaging operations, for which both resolution and maximum coverable area are critical aspects. The maximum attainable d under resolution constraint can be calculated as follows: d = h = \frac{\mathrm{GSD_{max}}}{2} \times \frac{f}{p} Where \mathrm{GSD_{max}} is the desired maximum ground sample distance, and all other variables are defined as above. Within this constraint, reducing the horizontal distance (d) without lowering the height (h) decreases the off-nadir angle and shifts the imaging closer to nadir, thereby improving the ground sample distance. Conversely, decreasing h while keeping d constant increases the off-nadir angle beyond 45°, which degrades the GSD. The 45° configuration provides the widest possible coverage while maintaining the specified GSD limit. == See also ==