How off-nadir imaging works:

Satellites are equipped with sensors that can adjust their viewing angles to capture images of areas not directly beneath them. This capability allows for increased revisit rates, enabling satellites to image specific locations more frequently without waiting for a direct overpass. By tilting their sensors, satellites can also acquire stereoscopic images from different angles, which are useful for creating 3D models of the Earth's surface.

Limitations and effects on imagery:

1. Geometric distortions: Tilting the sensor introduces geometric distortions, causing tall structures to appear to lean away from the image center. This effect, known as the "building-lean" phenomenon, can complicate accurate mapping and analysis.

2. Reduced spatial resolution: As the off-nadir angle increases, the distance between the satellite and the target area grows, leading to a decrease in image resolution. For instance, an image captured at a 0° off-nadir angle might have a resolution of 30 cm, whereas at a 30° angle, the resolution could degrade to around 40 cm.

3. Increased atmospheric interference: Observing the Earth's surface at higher off-nadir angles means the sensor's line of sight passes through more of the atmosphere, which can introduce additional scattering and absorption effects, potentially degrading image quality. 

4. Shadowing effects: Off-nadir viewing can result in longer shadows, especially in areas with tall structures or varied terrain. These shadows can obscure details and affect the interpretation of the imagery.

Positive applications of off-nadir imagery:

Despite all of their limitations off-nadir satellite images are useful in many areas. Examples?

• Earthquakes & landslides: – By combining multiple off-nadir images from different times, analysts can measure ground displacement and damage assessment in affected areas.
• Stereo imaging: Off-nadir images taken from two or more angles allow for the generation of digital elevation models (DEMs), which are essential for 3D city models.
• Building height estimation: The "leaning" effect seen in off-nadir images can actually be useful – it helps in calculating skyscraper heights and mapping shadow patterns.

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Maximum Off-Nadir Angles:

The feasible off-nadir angle varies depending on the satellite's design and mission objectives. For optical imagery, a typical maximum off-nadir angle is around 30 degrees. However, some satellites are capable of capturing images at greater angles. For example, the GeoEye-1 satellite can image up to 60 degrees off-nadir, allowing for more flexible imaging options at the cost of increased distortions and reduced resolution. 

In summary, while off-nadir imaging enhances a satellite's ability to monitor specific areas more frequently and from multiple perspectives, it also introduces certain limitations such as geometric distortions, reduced resolution and increased atmospheric interference. The choice of off-nadir angle must balance the need for timely and comprehensive data with the acceptable level of image quality degradation.