Dichroic Mirrors and Wavelength System Implementation

Overview

This document describes the implementation of dichroic mirrors and the wavelength-based color system for the optiverse optical simulation tool. This feature enables physically accurate simulation of wavelength-dependent optical elements and proper color representation based on spectral properties.

Features Implemented

1. Wavelength System

Source Wavelength Support

  • Sources can now be configured with a specific wavelength (in nanometers)
  • Two modes available:
    • Custom Color Mode: Traditional hex color picker (legacy behavior)
    • Wavelength Mode: Physical wavelength specification with automatic color computation

Wavelength-to-Color Conversion

  • Physically accurate conversion from wavelength to RGB colors
  • Based on the visible spectrum (380-750 nm)
  • Uses an improved approximation of CIE color matching functions
  • Handles UV (< 380 nm) and IR (> 750 nm) with appropriate visual representation

Common Laser Wavelength Presets

Predefined wavelengths for common laser sources:

  • UV (355nm Nd:YAG 3rd harmonic)
  • Violet (405nm diode)
  • Blue (450nm diode)
  • Cyan (488nm Ar-ion)
  • Green (532nm Nd:YAG 2nd harmonic)
  • Yellow (589nm sodium)
  • Red (633nm HeNe)
  • Deep Red (650nm diode)
  • IR (808nm diode)
  • IR (1064nm Nd:YAG fundamental)

2. Dichroic Mirrors

Physical Model

Dichroic mirrors use a wavelength-dependent reflection/transmission model:

R(λ) = 1 / (1 + exp((λ - λ_cutoff) / Δλ))
T(λ) = 1 - R(λ)

Where:

  • λ is the incident wavelength
  • λ_cutoff is the cutoff wavelength (50% transition point)
  • Δλ is the transition width (steepness of the transition)

Behavior:

  • Short wavelengths (λ < λ_cutoff): Reflected
  • Long wavelengths (λ > λ_cutoff): Transmitted
  • Transition region: Smooth sigmoid function

Component Properties

  • Cutoff Wavelength: The wavelength at which R = T = 50%
  • Transition Width: Width of the transition region (smaller = sharper cutoff)
  • Physical Size: Standard 1-inch optic (25.4 mm)
  • Default Angle: 45° for beam combining/splitting

Use Cases

  1. Wavelength Multiplexing: Combine multiple laser wavelengths onto a single beam path
  2. Beam Splitting by Color: Separate different wavelengths from a polychromatic source
  3. Fluorescence Applications: Separate excitation and emission wavelengths
  4. Multi-wavelength Interferometry: Wavelength-dependent beam paths

Architecture

Data Models

SourceParams

Extended with wavelength support:

@dataclass
class SourceParams:
    # ... existing fields ...
    wavelength_nm: float = 0.0  # 0 = use color_hex, >0 = compute from wavelength

DichroicParams

New model for dichroic mirrors:

@dataclass
class DichroicParams:
    x_mm: float = 0.0
    y_mm: float = 0.0
    angle_deg: float = 45.0
    object_height_mm: float = 80.0
    cutoff_wavelength_nm: float = 550.0  # Green cutoff
    transition_width_nm: float = 50.0    # Transition width
    image_path: Optional[str] = None
    mm_per_pixel: float = 0.1
    line_px: Optional[Tuple[float, float, float, float]] = None
    name: Optional[str] = None

OpticalElement

Extended to support dichroic properties:

@dataclass
class OpticalElement:
    kind: str  # 'lens' | 'mirror' | 'bs' | 'waveplate' | 'dichroic'
    # ... existing fields ...
    cutoff_wavelength_nm: float = 550.0
    transition_width_nm: float = 50.0

RayPath

Extended to carry wavelength information:

@dataclass
class RayPath:
    points: List[np.ndarray]
    rgba: Tuple[int, int, int, int]
    polarization: Optional[Polarization] = None
    wavelength_nm: float = 0.0  # Wavelength in nm (0 = not specified)

Ray Tracing

The ray tracing engine has been updated to:

  1. Propagate wavelength through the optical system
  2. Compute dichroic reflectance/transmittance based on wavelength
  3. Generate split rays (reflected and transmitted) with appropriate intensities
  4. Preserve polarization through dichroic interactions

Physics Implementation 

def compute_dichroic_reflectance(
    wavelength_nm: float,
    cutoff_wavelength_nm: float,
    transition_width_nm: float
) -> Tuple[float, float]:
    """
    Compute R and T for a dichroic mirror using sigmoid function.
    Returns (reflectance, transmittance).
    """
    delta = (wavelength_nm - cutoff_wavelength_nm) / max(1.0, transition_width_nm)
    reflectance = 1.0 / (1.0 + np.exp(delta))
    transmittance = 1.0 - reflectance
    return reflectance, transmittance

User Interface

Source Editor

The source editor now includes:

  • Color Mode dropdown: Choose between “Custom Color” and “Wavelength”
  • Wavelength Preset dropdown: Quick selection of common laser wavelengths
  • Wavelength spinbox: Fine control (200-2000 nm range)
  • Custom Color picker: Traditional hex color selection (disabled in wavelength mode)
  • Live color preview: Updates automatically based on wavelength or custom color

Dichroic Editor

Double-click a dichroic mirror to edit:

  • Position (X, Y coordinates)
  • Optical axis angle
  • Length (physical size)
  • Cutoff wavelength (200-2000 nm)
  • Transition width (1-200 nm)

Component Library

Dichroics appear in their own category in the component library dock:

  • Dichroics category
    • Dichroic Mirror (550nm cutoff) - standard green/red splitter

Usage Examples

Example 1: Wavelength Multiplexing

Goal: Combine red (633nm) and green (532nm) lasers onto a single path

  1. Add a green laser source (532nm)
    • Set wavelength to 532.0 nm (or use “Green (532nm Nd:YAG 2nd)” preset)
    • Position at (-400, 50)
    • Aim horizontally (0°)
  2. Add a red laser source (633nm)
    • Set wavelength to 633.0 nm (or use “Red (633nm HeNe)” preset)
    • Position at (0, -400)
    • Aim vertically (90°)
  3. Add a dichroic mirror (550nm cutoff)
    • Position at (0, 0)
    • Angle at 45°
    • The 532nm (green) light reflects, 633nm (red) transmits
    • Both beams exit along the same path

Example 2: Spectral Separation

Goal: Separate a multi-wavelength beam

  1. Create multiple sources at the same position with different wavelengths
    • Blue (450nm), Green (532nm), Red (650nm)
  2. Add dichroic mirrors at appropriate positions:
    • First dichroic at 500nm cutoff (separates blue from green+red)
    • Second dichroic at 590nm cutoff (separates green from red)
  3. Each wavelength exits in a different direction

Example 3: Fluorescence Simulation

Goal: Model excitation/emission separation

  1. Excitation source: 488nm (cyan/blue)
  2. Sample position with “emission” (simulate with 520nm green source)
  3. Dichroic at 510nm cutoff
    • Reflects 488nm excitation to sample
    • Transmits 520nm emission to detector

Technical Details

Color Conversion Algorithm

The wavelength-to-RGB conversion uses a piecewise linear approximation with gamma correction:

def wavelength_to_rgb(wavelength_nm: float) -> tuple[int, int, int]:
    """
    Convert wavelength (nm) to RGB using spectral approximation.
    
    Spectrum regions:
    - 380-440 nm: Violet to Blue
    - 440-490 nm: Blue to Cyan
    - 490-510 nm: Cyan to Green
    - 510-580 nm: Green to Yellow
    - 580-645 nm: Yellow to Red
    - 645-750 nm: Red (with intensity falloff)
    """
    # ... (see implementation in color_utils.py)

Dichroic Physics

The sigmoid transition function provides:

  • Energy conservation: R + T ≈ 1 at all wavelengths
  • Realistic transitions: Not infinitely sharp, has finite width
  • Physical accuracy: Matches real thin-film interference coatings

Transition width interpretation:

  • Small width (10-20 nm): Sharp cutoff (high-quality coating)
  • Medium width (50 nm): Standard dichroic
  • Large width (100+ nm): Broadband or color filter

Performance Considerations

  • Wavelength checking adds minimal overhead (single comparison per ray-element interaction)
  • Color computation happens once per source, cached for all rays
  • Dichroic splitting handled same as regular beamsplitters (bifurcation in ray tree)

Component Editor Integration

Creating Custom Dichroics

  1. Open Component Editor (Tools menu)
  2. Load or drop a dichroic mirror image
  3. Set component kind to “dichroic”
  4. Click two points on the optical element to calibrate
  5. Enter:
    • Physical height (object_height_mm)
    • Cutoff wavelength (cutoff_wavelength_nm)
    • Transition width (transition_width_nm)
  6. Save to library

Library Storage

Dichroic components serialize with these fields:

{
  "name": "Dichroic Mirror (550nm cutoff)",
  "kind": "dichroic",
  "cutoff_wavelength_nm": 550.0,
  "transition_width_nm": 50.0,
  "object_height_mm": 25.4,
  "image_path": "path/to/image.png",
  "line_px": [x1, y1, x2, y2],
  "angle_deg": 45.0
}

Future Enhancements

Possible extensions to this system:

  1. Wavelength-dependent refractive indices: Chromatic aberration in lenses
  2. Dispersion modeling: Prisms and gratings
  3. Bandpass filters: Transmission curves for optical filters
  4. Multi-band dichroics: Multiple cutoff wavelengths
  5. Polarization-dependent dichroics: Combine PBS and dichroic behavior
  6. Fluorescence sources: Wavelength conversion (e.g., 488nm → 520nm)

Testing

The implementation includes:

  • Unit tests for wavelength-to-RGB conversion
  • Validation of dichroic physics (energy conservation)
  • Integration tests for ray tracing with wavelength-dependent elements
  • UI tests for source editor wavelength controls

References

  1. Dan Bruton’s wavelength-to-RGB algorithm (improved version)
  2. CIE color matching functions
  3. Thin-film interference theory (dichroic coatings)
  4. Jones calculus for polarization

Summary

This implementation provides a physically accurate, user-friendly system for simulating wavelength-dependent optical systems. The dichroic mirrors enable realistic modeling of:

  • Laser beam combining
  • Spectral separation
  • Fluorescence microscopy
  • Multi-wavelength interferometry
  • Color-dependent beam routing

The wavelength system integrates seamlessly with existing polarization and ray tracing features, providing a comprehensive optical simulation environment.