Physics Validator

Validate optical physics parameters for PRISM instruments to ensure physically realistic configurations.

Purpose

Optical imaging simulations require careful parameter selection to produce physically meaningful results. This skill validates that instrument configurations respect fundamental optical physics constraints.

When to Use

Use this skill when:

• Configuring Telescope, Microscope, or Camera instruments
• Checking if parameters are physically realistic
• Validating diffraction regime (Fresnel vs Fraunhofer)
• Ensuring Nyquist sampling requirements are met
• Debugging unexpected simulation results
• Setting up new experiments or configurations

Validation Checks

1. Fresnel Number Analysis

The Fresnel number determines the diffraction regime:

# Fresnel number formula
F = d**2 / (wavelength * distance)

# where:
#   d = aperture diameter
#   wavelength = light wavelength
#   distance = propagation distance

Interpretation:

Fresnel Number	Regime	Propagation Method
F << 0.1	Fraunhofer (far-field)	FFT-based
F >> 10	Fresnel (near-field)	Angular Spectrum
0.1 <= F <= 10	Transition	Angular Spectrum recommended

PRISM Implementation:

from prism.config.constants import is_fraunhofer, is_fresnel

# Check diffraction regime
wavelength = 500e-9  # 500 nm
aperture_diameter = 0.1  # 10 cm
distance = 1000  # 1 km

fresnel_number = aperture_diameter**2 / (wavelength * distance)

if fresnel_number < 0.1:
    print("Fraunhofer regime - use FFT propagation")
elif fresnel_number > 10:
    print("Fresnel regime - use Angular Spectrum")
else:
    print("Transition regime - Angular Spectrum recommended")

2. Resolution Limits

Each instrument type has different resolution limits:

Telescope (Rayleigh Criterion)

# Angular resolution (radians)
theta_rayleigh = 1.22 * wavelength / diameter

# Spatial resolution at distance
resolution = 1.22 * wavelength * distance / diameter

# Example: 10cm aperture, 500nm light, 1km distance
# resolution = 1.22 * 500e-9 * 1000 / 0.1 = 6.1 mm

Microscope (Abbe Limit)

# Minimum resolvable feature
d_abbe = 0.61 * wavelength / NA

# where NA = numerical aperture = n * sin(theta)
# For air (n=1) with half-angle 60deg: NA = 0.866

# Example: 500nm light, NA=0.5
# d_abbe = 0.61 * 500e-9 / 0.5 = 610 nm

Camera (Airy Disk)

# Airy disk diameter
d_airy = 2.44 * wavelength * f_number

# where f_number = focal_length / aperture_diameter

# Example: 500nm light, f/2.8 lens
# d_airy = 2.44 * 500e-9 * 2.8 = 3.4 um

3. Nyquist Sampling

For proper sampling, pixel size must satisfy:

# Nyquist criterion
pixel_size <= resolution_limit / 2

# Examples:
# Telescope with 6mm resolution: pixel_size <= 3mm
# Microscope with 610nm resolution: pixel_size <= 305nm
# Camera with 3.4um Airy disk: pixel_size <= 1.7um

Validation Function:

def validate_nyquist(pixel_size: float, resolution_limit: float) -> bool:
    """Check if pixel size satisfies Nyquist criterion."""
    nyquist_limit = resolution_limit / 2
    is_valid = pixel_size <= nyquist_limit

    if not is_valid:
        print(f"WARNING: Pixel size {pixel_size:.2e} exceeds Nyquist limit {nyquist_limit:.2e}")
        print(f"  Aliasing may occur. Reduce pixel size or increase resolution limit.")

    return is_valid

4. Physical Parameter Ranges

Common valid ranges for optical parameters:

Parameter	Typical Range	Notes
Wavelength	300nm - 1100nm	Visible + near-IR
Telescope aperture	1cm - 10m	Small to large telescopes
Microscope NA	0.1 - 1.4	Air to oil immersion
Camera f-number	f/1.0 - f/22	Fast to slow lenses
SNR	10 - 1000	Typical imaging conditions

Validation:

def validate_wavelength(wavelength: float) -> bool:
    """Validate wavelength is in reasonable range."""
    if not (100e-9 <= wavelength <= 10e-6):
        print(f"WARNING: Wavelength {wavelength:.2e} outside typical range (100nm - 10um)")
        return False
    return True

def validate_numerical_aperture(na: float) -> bool:
    """Validate NA is physically possible."""
    if not (0 < na <= 1.5):  # 1.5 for oil immersion
        print(f"WARNING: NA {na} is physically impossible (must be 0 < NA <= 1.5)")
        return False
    return True

5. Depth of Field

For 3D imaging, check depth of field:

# Microscope depth of field
DOF_microscope = wavelength / NA**2

# Camera depth of field (approximate)
DOF_camera = 2 * f_number * wavelength * (magnification + 1)**2

# Example: 500nm, NA=0.5
# DOF = 500e-9 / 0.25 = 2 um

Complete Validation Workflow

def validate_telescope_config(config: dict) -> list[str]:
    """Validate telescope configuration."""
    issues = []

    wavelength = config['wavelength']
    diameter = config['aperture_diameter']
    distance = config['distance']
    pixel_size = config.get('pixel_size')

    # 1. Check wavelength
    if not (100e-9 <= wavelength <= 10e-6):
        issues.append(f"Wavelength {wavelength:.2e} outside typical range")

    # 2. Check Fresnel number
    F = diameter**2 / (wavelength * distance)
    if 0.1 <= F <= 10:
        issues.append(f"Fresnel number {F:.2f} in transition regime - results may be approximate")

    # 3. Check resolution
    resolution = 1.22 * wavelength * distance / diameter

    # 4. Check Nyquist (if pixel size provided)
    if pixel_size and pixel_size > resolution / 2:
        issues.append(f"Pixel size {pixel_size:.2e} violates Nyquist (limit: {resolution/2:.2e})")

    # 5. Check aperture size
    if diameter > distance / 10:
        issues.append(f"Aperture {diameter} may be too large for distance {distance}")

    return issues


def validate_microscope_config(config: dict) -> list[str]:
    """Validate microscope configuration."""
    issues = []

    wavelength = config['wavelength']
    na = config['numerical_aperture']
    pixel_size = config.get('pixel_size')

    # 1. Check NA
    if not (0 < na <= 1.5):
        issues.append(f"NA {na} is physically impossible")

    # 2. Check resolution
    resolution = 0.61 * wavelength / na

    # 3. Check Nyquist
    if pixel_size and pixel_size > resolution / 2:
        issues.append(f"Pixel size {pixel_size:.2e} violates Nyquist (limit: {resolution/2:.2e})")

    # 4. Check depth of field
    dof = wavelength / na**2
    if dof < 100e-9:
        issues.append(f"Very shallow DOF ({dof:.2e}m) - focus stability critical")

    return issues

Common Issues and Solutions

Issue 1: Aliasing Artifacts

Symptoms: Rings, moiré patterns, or jagged edges in reconstruction Cause: Pixel size too large (Nyquist violation) Solution: Reduce pixel size or use anti-aliasing

Issue 2: Missing High Frequencies

Symptoms: Blurry reconstruction, loss of fine detail Cause: Aperture too small, resolution limit too coarse Solution: Increase aperture size or reduce wavelength

Issue 3: Incorrect Diffraction Pattern

Symptoms: Wrong PSF shape, unexpected propagation behavior Cause: Using wrong propagation method for Fresnel number Solution: Check Fresnel number and select appropriate method

Issue 4: Numerical Instabilities

Symptoms: NaN values, diverging iterations Cause: Parameters outside valid range Solution: Validate all parameters before simulation

Quick Reference

Fresnel Number

F = d² / (λ × z)
F < 0.1 → Far-field (Fraunhofer)
F > 10  → Near-field (Fresnel)

Resolution Formulas

Telescope:  θ = 1.22 λ/D,  δ = 1.22 λz/D
Microscope: d = 0.61 λ/NA
Camera:     d = 2.44 λ × f/#

Nyquist

pixel_size ≤ resolution_limit / 2

Related Skills

• torch-shape-validator: Validate tensor dimensions in optical computations
• complex-tensor-handler: Handle complex-valued fields in Fourier optics
• unit-test-generator: Create tests for physics validation functions

Checklist

Before running simulations:

• Wavelength in valid range (100nm - 10um)
• Fresnel number checked, appropriate propagation selected
• Resolution limit calculated for instrument type
• Nyquist sampling satisfied
• Aperture/NA in physical range
• Depth of field adequate for sample thickness
• SNR appropriate for detection conditions