Parallax–height relationship – choose the correct derivative form In stereophotogrammetry, if p is the absolute stereoscopic parallax of a point at elevation h, baseline B, camera focal length f, and flying height above datum H, then the rate of change of parallax with respect to elevation (dp/dh) is:

Introduction / Context:
Absolute stereoscopic parallax is the key measurable used to derive elevations from overlapping aerial photographs. Understanding how parallax changes with elevation (dp/dh) allows us to quantify vertical precision and design suitable flying heights and baselines for a required mapping accuracy.

Given Data / Assumptions:

• Frame camera of focal length f.
• Airbase (exposure station spacing) B along the flight direction.
• Flying height above the chosen datum H.
• Small-tilt or vertical photography so that the standard parallax–height relation holds.

Concept / Approach:

For vertical/near-vertical photos, the absolute stereoscopic parallax p for a point at elevation h obeys the proportionality p ∝ fB / (H - h). Differentiating p with respect to h (treating other quantities as constants) gives a square dependence on the denominator: dp/dh = fB / (H - h)^2. The negative sign is implicit if one tracks the fact that as h increases (point higher), the denominator (H - h) decreases and parallax increases; however, the magnitude of the sensitivity is fB / (H - h)^2 and is the standard form used for precision analysis.

Step-by-Step Solution:

Verification / Alternative check:

Dimension check: f and B have dimensions of length, (H - h) has length; therefore dp/dh has dimensions of dimensionless per length as expected for a change in image displacement per unit height.

Why Other Options Are Wrong:

• Options (a), (c), and (d) have incorrect dependency on (H - h) or wrongly use (H + h).
• Option (e) mixes terms and units improperly.

Common Pitfalls:

Forgetting that precision worsens as the ground clearance (H - h) decreases; ignoring that baseline B and focal length f directly improve height sensitivity (larger B and f increase dp/dh).

Final Answer:

fB / (H - h)^2