Angular Resolution

Short Description of Topic

The Main Idea

Angular Resolution is the ability of a device to visibly separate two different objects in space that are located a close angular distance to each other. The closer the objects are while the device can still see distinguish between them, the higher the angular resolution is.

Angular resolution is also referred to as spatial resolution.

A Mathematical Model

The equation for angular resolution is [math]\displaystyle{ {∆θ = \frac{λ}{W}} }[/math] where W is the width of the device

A Computational Model

The top most image demonstrates the highest angular resolution. It is most able to differentiate between the two objects. The bottom image demonstrates the lowest angular resolution. It is unable to differentiate between the two objects.

Summary of Derivation

The maximum for angular momentum is the spot at which it is the brightest. The mimumum is the spot at which it is the darkest. The maximum is at angle θ while the minimum is at angle (θ + ∆θ). A minimum can only occur if light is passing through the first slit and the middle slit of width of the device. This results in a path difference of [math]\displaystyle{ {\frac{Nλ}{2}} }[/math] for the maximum [math]\displaystyle{ {\frac{Nλ}{2} + \frac{λ}{2}} }[/math] for the minimum. Through a series of trig identities, is was discovered that the angular half width of a maximum is [math]\displaystyle{ {∆θ = \frac{λ}{W}} }[/math]. This result is the definition of angular resolution.

Examples

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