Gerchberg–Saxton Phase Retrieval
Run a bounded one-dimensional Gerchberg–Saxton phase-retrieval iteration.
Description
Gerchberg–Saxton phase retrieval alternates amplitude constraints in two Fourier-related planes.
Gerchberg–Saxton phase retrieval alternates amplitude constraints in two Fourier-related planes. Here the data are one-dimensional amplitudes and initial source phase is zero.1
Run a bounded one-dimensional Gerchberg–Saxton phase-retrieval iteration.
When to use Gerchberg–Saxton Phase Retrieval
Use this tool to run a bounded one-dimensional Gerchberg–Saxton phase-retrieval iteration.
Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
How to use Gerchberg–Saxton Phase Retrieval and understand its results
- Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
- Enter sourceAmplitude, targetAmplitude, iterations using the field table and calculation rules, then run the tool.
- Read sourcePhaseRadians, finalTargetAmplitude. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| sourceAmplitude | Source-plane amplitudes | list of number | Required |
| targetAmplitude | Target-plane amplitudes | list of number | Required |
| iterations | Iteration count | integer; minimum: 1; maximum: 100 | Required |
Enter nonempty aligned nonnegative source/target amplitudes and integer iterations 1–100. Use direct DFT and inverse DFT divided by n, repeatedly enforce target amplitude and restore source amplitude. Return source phase and final target amplitude.
phase←arg(IDFT(targetAmplitude×exp(i arg(DFT(sourceAmplitude×exp(i phase)))))) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| sourcePhaseRadians | Retrieved source phase (rad) | list of number |
| finalTargetAmplitude | Final target-plane amplitudes | list of number |
{
"input": {
"sourceAmplitude": [
1,
1
],
"targetAmplitude": [
2,
0
],
"iterations": 1
},
"output": {
"sourcePhaseRadians": [
0,
0
],
"finalTargetAmplitude": [
2,
1.2246467991473532e-16
]
}
}Limitations and assumptions
No convergence criterion or uniqueness guarantee is provided. All-zero amplitudes are accepted. Cost scales as iterations×n², so use short scoped arrays.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use THz Waveform Spectrum: Compute a direct discrete magnitude spectrum from a THz time-domain waveform. For a complementary task, use Optical Phased-Array Steering: Calculate phased-array beam steering from wavelength, element spacing, and adjacent phase shift.
References
-
Gerchberg–Saxton Phase Retrieval — tool.io
Similar or alternative tools
- THz Waveform Spectrum
Compute a direct discrete magnitude spectrum from a THz time-domain waveform.
- Optical Phased-Array Steering
Calculate phased-array beam steering from wavelength, element spacing, and adjacent phase shift.