Monday, July 11, 2011

How to Calculate Angular Resolution

Angular resolution, also known as the Rayleigh criterion and spatial resolution, is the minimum angular distance between two distant objects that an instrument can discern resolvable detail. As an example, if a person holds two pens 10cm apart and stands 2m from you, you can discern there are two pencils. As the other person moves away, the pencils appear to move closer together or the angular separation decreases. The calculation of this angle is very important in optics. This angle represents the resolve power and precision of optical instruments such as your eye, a camera and even a microscope.


#1 Write down sin A = 1.220 (W ÷ D). This formula is known as the angular resolution formula and is the mathematical representation of the Rayleigh criterion. The Rayleigh criterion basically says that two different points are resolved when the diffraction maximum of one image coincides with the first minimum diffraction of a second image. If the distance is greater, the two points are resolved and if it is smaller they are not resolved.

# 2 Calculate the wavelength of the light waves used to focus the image. This number is represented by W in the angular resolution formula. For example, say you are using yellow light. The wavelength for yellow light is about 577nm. This number can be looked up. To get a more precise answer you will need to know the frequency of the light you are using and the speed of light. The wavelength equation is wavelength (W) = speed of light (c) ÷ frequency (f).

# 3 Find the value of the entrance pupil diameter (D) or the diameter of the lens aperture (D) of the imaging system you are using. For telescopes and most other optical instruments, the diameter of the aperture can be found in the user manual or you can contact the manufacturer who will be able to tell you the correct value.

# 4 Rewrite the formula substituting the wavelength (W) value and the diameter (D) value you just found.

# 5 Ensure your wavelength and diameter have been converted into the same units of measure. For example, if your wavelength is in meters than your diameter needs to be converted to meters or visa versa.

# 6 Manipulate the formula to solve for A by dividing both sides of the equation by sin. The manipulated formula should appear as the following A = arc sin [1.220(W ÷ D)].

# 7 Use your calculator to do the math to find out what the angular resolution (A) is equal to. The units of the wavelength and the diameter cancel so the answer is expressed in radians. For astronomy purposes you can convert radians to seconds of arc

Wednesday, April 13, 2011

Angular Resolution

Angular resolution is the minimum angular separation at which two equal targets can be separated when at the same range. The angular resolution characteristics of a radar are determined by the antenna beam width represented by the -3 dB angle Θ which is defined by the half-power (-3 dB) points.

The half-power points of the antenna radiation pattern (i.e. the -3 dB beam width) are normally specified as the limits of the antenna beam width for the purpose of defining angular resolution; two identical targets at the same distance are, therefore, resolved in angle if they are separated by more than the antenna -3 dB beam width.

An important remark has to be made immediately: the smaller the beam width Θ, the higher the directivity of the radar antenna. The angular resolution as a distance between two targets calculate the following formula:

SA ≥ 2R · sin Θ with Θ = antenna beam width (Theta)
SA = angular resolution
as a distance between two targets
R = slant range aim - antenna [m] (1)

The angular resolution of targets on an analogue PPI display, in practical terms, is dependent on the operator being able to distinguish the two targets involved. Systems having Target-Recognition feature can improve their angular resolution. Cause such systems are able to compare indivual Target-Pulse-Amplitudes.

Tuesday, March 8, 2011

Clues from High Angular Resolution Observations

Francesca Bacciotti, Emma Whelan, Leonardo Testi (Editors) | 2007-01-01 00:00:00 | Springer; 1 edition | 291 | Astronomy and Cosmology

This volume contains the edited lecture notes of the Second JETSET School on Jets from Young Stars: Clues from High Angular Resolution Observations organised by the Marie Curie Research Training Network JETSET: Jet Simulations, Experiments and Theory.

After the opening two chapters on jet emission, readers can learn the fundamental background of modern high-spatial-resolution techniques, and how such methods have impacted on our understanding of young stars.

The lectures provide hands-on insight into Observing from space, e.g. from HST and in the future JWST, and from the ground with adaptive optics.

The use of interferometers at millimetre and infrared wavelengths, Spectro-astrometry, Image analysis and spectral diagnostic techniques, High-Angular Resolution studies of the inner regions of circumstellar disks which play a fundamental role in jet launching.

The books' practical approach makes it an outstanding and extremely useful textbook for PhD students and young researchers in astronomy.