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Theory vs. Simulation: Exploring Diffraction Through a Circular Aperture

Ansys Zemax

Diffraction is a fundamental optical phenomenon that occurs when light interacts with an obstacle or aperture, bending and spreading rather than traveling in a straight line. This effect plays a crucial role in imaging, laser optics, and wavefront propagation, where precise control of light behavior is essential. Accurately understanding diffraction patterns is key to optimizing optical system performance, reducing aberrations, and improving image quality in various applications.

While theoretical models provide a foundation for understanding diffraction, simulation tools like Ansys Zemax allow optical engineers to visualize, analyze, and optimize optical systems before physical prototyping. This blog explores the diffraction of light through a circular aperture by comparing classical theoretical predictions with Zemax simulations, demonstrating how simulations complement and enhance optical design processes.

Theoretical Background:

Diffraction through a circular aperture is best described by the Airy pattern, named after George Biddell Airy. When a plane wave passes through a circular aperture, it produces a characteristic diffraction pattern composed of:

  • A central bright spot known as the Airy disk, which contains the majority of the diffracted light energy.
  • Concentric rings of decreasing intensity, which result from constructive and destructive interference of the wavefronts.
  • A well-defined angular resolution limit, governed by the Rayleigh criterion, which determines the minimum resolvable feature size in imaging systems.

Ideal Airy Disc pattern (Ref. – Optics by Ajoy Ghatak, 3rd edition)

Theoretical Calculations

The Setup used:
Collimated beam of size larger than pinhole is incident on the pinhole and the parameters of the Fresnel diffraction setup are:
Pinhole size, d = 200 µm

Distance between projection screen & pinhole, D = 300 mm

Wavelength, λ = 532 nm
Inputs given as per the considered setup in “Circular Aperture Diffraction from hyperphysics” Ref. article used Circular Aperture Diffraction from hyperphysics
Theoretical calculations provided upto 3rd order “Circular Aperture Diffraction from hyperphysics”

Simulating Diffraction in Zemax

Zemax offers powerful tools for modelling diffraction effects using both physical optics propagation (POP) and wavefront analysis. To simulate diffraction through a circular aperture:

1. Setup the Optical System

  • Define a monochromatic source with a plane wavefront.
  • Insert a circular aperture stop.
  • Configure the system for wave optics analysis.

2. Run Physical Optics Propagation (POP)

  • Use the POP tool to propagate the wavefront through the aperture.
  • Observe the intensity distribution on the projection screen kept at a particular distance after pinhole.
  • Compare the simulated Airy disk with the theoretical model.

3. Analyze Results

  • Measure the central maximum intensity and ring spacing.
  • Compare the simulated first dark ring location with theoretical predictions.
  • Evaluate the effects of wavelength, aperture size, and focal length on diffraction patterns.

Zemax Simulation Setup, Analysis & Result Interpretation:

3D layout – Collimated monochromatic light incident on 200 µm pinhole, and a ray emerging out of pinhole hitting the observation screen at 300 mm after pinhole.

Collimated light Incident on pinhole

Zoomed in view of 200 µm pinhole

Diffraction pattern as observed in POP analysis at 300 mm after the pinhole.

X & Y-axis are screen dimensions in mm.

Diffraction pattern cross section to observe the placement of maxima & minima points on the observation screen.

X-axis is in mm & Y-axis (peak irradiance) is in watts/mm2.

Results as per simulation
Order
Minima
Maxima
m value
Displacement Y (mm)
m value
Displacement Y (mm)
1
1.22
0.9793
1.635
1.313
2
2.233
1.778
2.679
2.129
3
3.238
2.572
3.69
2.910

Zoomed in snap of POP analysis for 1st, 2nd & 3rd order positions of minima & maxima

Zoomed in snap of POP analysis for noting the 1st order minima, readout taken from X coordinate readout displayed at top of graph after placing the cursor at the minima point (dip).

Comparison Theory vs. Simulation
Order
Minima
Maxima
m value
Displacement Y (mm) Theory
Displacement Y (mm) Simulation
m value
Displacement Y (mm) Theory
Displacement Y (mm) Simulation
1
1.22
0.9735
0.9793
1.635
1.304
1.313
2
2.233
1.781
1.778
2.679
2.137
2.129
3
3.238
2.584
2.572
3.69
2.944
2.910

Theory vs. Simulation: Key Insights

  • The Airy disk size and ring structure closely match theoretical expectations.
  • Minor deviations arise due to numerical approximations and sampling resolution in Zemax.
  • The simulation allows for dynamic modifications, enabling optimization for real-world optical designs.
  • The impact of aberrations, partial coherence, and lens imperfections can be studied in Zemax, extending beyond the ideal theoretical model.

Conclusion

Understanding and controlling diffraction is critical in optical engineering, particularly in applications like microscopy, laser beam shaping, astronomy, and imaging systems. While theoretical principles lay the groundwork, Ansys Zemax simulations provide a practical and visual approach to verifying and refining optical designs.

By integrating simulation with theoretical analysis, engineers can bridge the gap between fundamental physics and real-world implementation, leading to more efficient, high-performance optical systems. Whether refining lens apertures, optimizing diffraction gratings, or enhancing laser beam propagation, Zemax enables innovation in optical design through accurate, simulation-driven insights.

Are you from a startup looking to gain actionable strategies to improve design efficiency and bring cutting-edge optical products to market with confidence using Ansys Zemax? Then register now for our upcoming webinar

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