For a 1.2 m prime-focus parabolic dish, the beamwidth depends mainly on the operating frequency (or wavelength), not strongly on the F/D ratio. A typical prime-focus dish has an F/D between about 0.3 and 0.45.
A commonly used approximation for the half-power beamwidth (HPBW) is:
where:
- θHPBW = beamwidth in degrees
- λ = wavelength in metres
- D = dish diameter in metres
For a 1.2 m dish:
| Frequency | Wavelength | HPBW |
|---|---|---|
| 1.42 GHz (Hydrogen line) | 0.211 m | ~12.3° |
| 2.4 GHz | 0.125 m | ~7.3° |
| 10 GHz | 0.030 m | ~1.75° |
| 12 GHz | 0.025 m | ~1.46° |
For your radio astronomy work at 1420.405 MHz:
- Diameter = 1.2 m
- Wavelength = 0.211 m
HPBW ≈ 70 × 0.211 / 1.2 ≈ 12.3°
A more realistic value, depending on illumination taper and feed design, is typically 11°–13°.
The F/D ratio affects the feed geometry and illumination efficiency, but only has a small effect on the final beamwidth compared with the dish diameter and frequency.
Perform calculation for 22GHz for maser observations.
For the water maser line at 22.23508 GHz:
Frequency, f = 22.235 GHz
Dish diameter, D = 1.2 m
First calculate the wavelength:
lambda = c / f
Using c = 299,792,458 m/s:
lambda = 0.01348 m = 13.48 mm
Now apply the beamwidth approximation:
HPBW ~= 70 * lambda / D
HPBW ~= 70 * 0.01348 / 1.2
HPBW ~= 0.79 degrees
which is approximately:
47 arcminutes
2,840 arcseconds
Using the more rigorous expression often used for radio telescopes:
HPBW ~= 58 * lambda / D
gives:
HPBW ~= 0.65 degrees (39 arcminutes)
Therefore a practical estimate for a real 1.2 m dish at 22 GHz is:
Beamwidth ~= 0.65 to 0.8 degrees
Expected Gain
Gain = eta * (pi * D / lambda)^2
Assuming:
Aperture efficiency eta = 0.55
D = 1.2 m
lambda = 0.01348 m
D/lambda ~= 89.0
Gain ~= 43,000 (linear)
Gain(dBi) = 10 * log10(Gain)
Gain ~= 46.3 dBi
Pointing Accuracy
For useful maser observations, pointing errors should ideally be less than about one-tenth of the beamwidth:
0.1 * 0.7 degrees ~= 0.07 degrees
which is:
about 4 arcminutes
about 240 arcseconds
Suitability for Water Maser Work
A 1.2 m dish can detect the strongest Galactic water masers if:
The feed and LNA are optimized for 22 GHz.
System temperature is kept low.
Long integrations are used.
Pointing is accurate to a few arcminutes.
Compared with a 3 m dish:
Signal power ratio = (1.2 / 3.0)^2
= 0.16
so a 3 m dish collects about 6.25 times more signal power.
Strong maser targets include Orion KL, W49A, and W51. A well-constructed 1.2 m system operating at 22 GHz may detect these sources, although integration times will be significantly longer than with a larger dish.