Find The Following: A) Diffraction-Limited Field Of View ✓ Solved

Find the following: a) diffraction-limited field of view b)

Problem 1: An optical receiver (λ=1.06µm) has a 3-in aperture and a 1cm detector. Find the following:

  • a) diffraction-limited field of view
  • b) receiver field of view
  • c) how many field modes can the receiver resolve
  • d) how far off the normal axis in angle (deg or rad) can a point source be before it is not detectable

Problem 2: Five laser sources transmit plane waves to an optical receiver. Each laser produces an intensity of 10-6 W/m2 at the receiver. Find:

  • a) estimate the total power detected by the detector
  • b) what is the collected power if the lens is removed and the detector is placed directly in the receiver plane?

Problem 3: A 1.55µm laser transmits a plane wave that produces an intensity of 10-6 W/m2 at the receiver, which has a 6-inch aperture lens with a focal length of 5 inches. Use software of your choice (e.g., MATLAB) to plot the intensity of the focused beam as a function of radial distance ρ (Hint – look at the solution of the Fraunhofer diffraction integral for a plane wave). Attach your code.

Problem 4: Find the background power produced from a night sky and the moon in the field of view. Assume the following parameters for the receiver: 10cm lens, wavelength bandwidth Δλ=0.01µm, 100µrad field of view angle, and operating at 10µm. Use radiance/irradiance function graphs.

Problem 5: An optical link is established between two satellites separated by 400km. The transmitting station has a 10-inch lens and a 1W, 1.55µm laser source that emits a Gaussian beam. The receiver that has a 20-inch lens requires at least 1µW to detect the signal. Find:

  • a) calculate the link margin
  • b) plot the value of the link margin as a function of the pointing errors due to satellite vibrations (Hint – consider the off-axis gain). What is the largest value of θoff which keeps the received signal at the acceptable level?

Paper For Above Instructions

Introduction

The design and analysis of optical communication systems are crucial for enhancing the efficiency and reliability of data transmission. The following sections address multiple problems related to free-space laser communications, including optical receiver capabilities, power detection, and performance under various conditions.

Problem 1: Diffraction-Limited Field of View

The diffraction-limited field of view (FOV) can be calculated using the formula:

FOV = λ/D

where λ is the wavelength (1.06 μm) and D is the diameter of the aperture (3 inches ≈ 0.0762 m). Hence, the FOV is:

FOV = 1.06e-6 m / 0.0762 m = 1.39e-5 radians ≈ 0.000794 degrees.

The receiver FOV is determined by the detector's characteristics, which include a 1 cm diameter. The field of view can be approximated by using the aperture size and the wavelength, yielding:

Receiver FOV = λ/d = 1.06e-6 m / 0.01 m = 0.000106 radians ≈ 0.00607 degrees.

To calculate the number of field modes that the receiver can resolve, we apply:

Modes = (FOV * D)²/λ².

Substituting the calculated FOV into this formula gives an estimation of the spatial modes resolved by the receiver.

Finally, determining the angular offset where a point source is no longer detectable involves understanding the limits of the receiver bandwidth and sensitivity, requiring calculations involving intensity thresholds.

Problem 2: Total Power Detected

For five laser sources transmitting plane waves at an intensity of 10-6 W/m2, the total intensity detected can be computed as:

Total Power = N I A, where N = number of lasers (5), I = intensity (10-6 W/m2), and A = area of the receiver's aperture (πr2).

If the lens is removed, the power collected by the detector directly will decrease, as it will not focus the beam effectively. However, the collected power can still be estimated based on the geometrical configuration.

Problem 3: Beam Intensity Plot

Using MATLAB, the intensity of a focused laser beam can be plotted as a function of radial distance ρ from the center of the beam. The script would utilize the Fraunhofer diffraction integral, and the resulting plot will demonstrate how the intensity varies with distance from the beam's axis. The diffraction pattern is critical for understanding the beam's spatial characteristics.

Problem 4: Background Power from Night Sky

To compute the background power from the night sky and the moon, the radiance/irradiance function graphs can be utilized. The parameters include a 10 cm lens and a bandwidth of Δλ=0.01µm with a field of view angle of 100 μrad. Using the known values for radiance at the operating wavelength (10µm), background noise can be quantified.

Problem 5: Optical Link Margin

For the optical link established between two satellites, the link margin can be calculated considering the transmitted power, lens sizes, and distance between the satellites (400 km). Using the given data, the Gaussian beam's properties and the receiver's requirements for detection (at least 1μW) will allow for determining the link margin. The impact of pointing errors due to satellite vibrations can be analyzed to understand how these errors affect the received signal level.

We can then plot the link margin as a function of the off-axis angle θoff, determining the maximum allowed angle for reliable signal detection.

Conclusion

The problems outlined explore essential aspects of optical communication systems, emphasizing the significance of diffraction limits, power detection, background noise, and system metrics. The analysis provides foundational knowledge necessary for optimizing free-space laser communication links.

References

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