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# Constants and Standards
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Colormath provides comprehensive collections of color science constants, illuminants, observers, density standards, and spectral data that serve as the foundation for accurate color calculations throughout the library.
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## Capabilities
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### Color Constants
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Fundamental mathematical constants used in CIE color calculations.
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```python { .api }
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# CIE constants
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CIE_E: float = 216.0/24389.0    # CIE epsilon constant
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CIE_K: float = 24389.0/27.0     # CIE kappa constant
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# Usage in Lab/XYZ conversions and other CIE calculations
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```
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### Illuminant Data
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Comprehensive illuminant XYZ values for different observer angles and standard illuminants.
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```python { .api }
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ILLUMINANTS: dict = {
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    '2': {  # 2-degree observer
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        'd65': (0.95047, 1.00000, 1.08883),
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        'd50': (0.96422, 1.00000, 0.82521),
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        'a': (1.09850, 1.00000, 0.35585),
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        'c': (0.98074, 1.00000, 1.18232),
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        'e': (1.00000, 1.00000, 1.00000),
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        # ... additional illuminants
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    },
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    '10': {  # 10-degree observer
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        'd65': (0.94811, 1.00000, 1.07304),
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        'd50': (0.96720, 1.00000, 0.81427),
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        'a': (1.11144, 1.00000, 0.35200),
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        'c': (0.97285, 1.00000, 1.16145),
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        'e': (1.00000, 1.00000, 1.00000),
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        # ... additional illuminants
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    }
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}
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OBSERVERS: list = ['2', '10']  # Available observer angles
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```
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### Chromatic Adaptation Matrices
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Transformation matrices for chromatic adaptation between different illuminants.
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```python { .api }
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ADAPTATION_MATRICES: dict = {
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    'bradford': {
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        'M': [[0.8951, 0.2664, -0.1614],
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              [-0.7502, 1.7135, 0.0367],
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              [0.0389, -0.0685, 1.0296]],
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        'M_inv': [[0.9869929, -0.1470543, 0.1599627],
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                  [0.4323053, 0.5183603, 0.0492912],
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                  [-0.0085287, 0.0400428, 0.9684867]]
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    },
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    'von_kries': {
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        'M': [[0.4002400, 0.7076000, -0.0808100],
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              [-0.2280000, 1.1500000, 0.0612000],
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              [0.0000000, 0.0000000, 0.9184000]],
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        'M_inv': [[1.8599364, -1.1293816, 0.2198974],
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                  [0.3611914, 0.6388125, -0.0000064],  
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                  [0.0000000, 0.0000000, 1.0888251]]
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    }
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    # ... additional adaptation methods
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}
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```
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## Density Standards
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### ANSI Status T Standards
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Transmission density standards for color reproduction.
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```python { .api }
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# ANSI Status T Red
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ANSI_STATUS_T_RED: dict = {
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    # Spectral response data for Status T Red filter
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    # Wavelength data from 340-830nm
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}
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# ANSI Status T Green  
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ANSI_STATUS_T_GREEN: dict = {
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    # Spectral response data for Status T Green filter
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}
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# ANSI Status T Blue
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ANSI_STATUS_T_BLUE: dict = {
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    # Spectral response data for Status T Blue filter
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}
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```
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### ANSI Status A Standards
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Reflection density standards for printing applications.
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```python { .api }
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# ANSI Status A Red
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ANSI_STATUS_A_RED: dict = {
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    # Spectral response data for Status A Red filter
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}
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# ANSI Status A Green
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ANSI_STATUS_A_GREEN: dict = {
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    # Spectral response data for Status A Green filter  
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}
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# ANSI Status A Blue
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ANSI_STATUS_A_BLUE: dict = {
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    # Spectral response data for Status A Blue filter
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}
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```
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### ANSI Status E Standards
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Photographic density standards.
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```python { .api }
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# ANSI Status E Red
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ANSI_STATUS_E_RED: dict = {
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    # Spectral response data for Status E Red filter
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}
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# ANSI Status E Green
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ANSI_STATUS_E_GREEN: dict = {
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    # Spectral response data for Status E Green filter
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}
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# ANSI Status E Blue  
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ANSI_STATUS_E_BLUE: dict = {
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    # Spectral response data for Status E Blue filter
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}
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```
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### ANSI Status M Standards
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Motion picture density standards.
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```python { .api }
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# ANSI Status M Red
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ANSI_STATUS_M_RED: dict = {
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    # Spectral response data for Status M Red filter
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}
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# ANSI Status M Green
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ANSI_STATUS_M_GREEN: dict = {
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    # Spectral response data for Status M Green filter
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}
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# ANSI Status M Blue
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ANSI_STATUS_M_BLUE: dict = {
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    # Spectral response data for Status M Blue filter
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}
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```
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### ISO Visual Standards
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Visual density standards for human visual assessment.
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```python { .api }
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# ISO Visual density standard
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ISO_VISUAL: dict = {
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    # Spectral response data matching human visual response
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}
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# Visual density threshold for automatic standard selection
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VISUAL_DENSITY_THRESH: float = 0.08
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```
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## Spectral Reference Data
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### Reference Illuminants
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Complete spectral power distributions for standard illuminants.
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```python { .api }
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# Reference illuminant A (tungsten)
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REFERENCE_ILLUM_A: dict = {
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    # Spectral power distribution data 340-830nm
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}
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# Reference illuminant B (direct sunlight)
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REFERENCE_ILLUM_B: dict = {
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    # Spectral power distribution data 340-830nm
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}
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# Reference illuminant C (average daylight)
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REFERENCE_ILLUM_C: dict = {
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    # Spectral power distribution data 340-830nm
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}
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# Reference illuminant E (equal energy)
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REFERENCE_ILLUM_E: dict = {
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    # Equal energy spectral distribution
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}
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# Blackbody illuminant data
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REFERENCE_ILLUM_BLACKBODY: dict = {
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    # Blackbody spectral data for various temperatures
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}
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# Reference illuminant lookup table
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REF_ILLUM_TABLE: dict = {
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    'a': REFERENCE_ILLUM_A,
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    'b': REFERENCE_ILLUM_B,  
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    'c': REFERENCE_ILLUM_C,
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    'e': REFERENCE_ILLUM_E
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}
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```
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## Usage Examples
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### Working with Illuminants
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```python
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from colormath.color_constants import ILLUMINANTS, OBSERVERS
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from colormath.color_objects import XYZColor
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# Get illuminant XYZ values
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d65_xyz_2deg = ILLUMINANTS['2']['d65']
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d65_xyz_10deg = ILLUMINANTS['10']['d65']
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print(f"D65 2°: X={d65_xyz_2deg[0]:.5f}, Y={d65_xyz_2deg[1]:.5f}, Z={d65_xyz_2deg[2]:.5f}")
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# Available observers
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print(f"Available observers: {OBSERVERS}")
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# Create XYZ color with specific illuminant
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xyz_color = XYZColor(xyz_x=0.4, xyz_y=0.3, xyz_z=0.2, illuminant='d50', observer='10')
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illum_xyz = xyz_color.get_illuminant_xyz()
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```
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### Using CIE Constants
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```python
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from colormath.color_constants import CIE_E, CIE_K
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# Example of using CIE constants in Lab calculations
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def xyz_to_lab_component(value, white_point):
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    """Example showing CIE constant usage."""
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    ratio = value / white_point
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    if ratio > CIE_E:
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        return ratio ** (1/3)
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    else:
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        return (CIE_K * ratio + 16) / 116
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# Use in calculations
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xyz_y = 0.18
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white_y = 1.0
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lab_f_y = xyz_to_lab_component(xyz_y, white_y)
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```
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### Density Standards Selection
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```python
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from colormath.density_standards import *
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from colormath.density import ansi_density
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# Dictionary of available standards
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density_standards = {
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    'Status T': {
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        'red': ANSI_STATUS_T_RED,
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        'green': ANSI_STATUS_T_GREEN,
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        'blue': ANSI_STATUS_T_BLUE
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    },
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    'Status A': {
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        'red': ANSI_STATUS_A_RED,
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        'green': ANSI_STATUS_A_GREEN,
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        'blue': ANSI_STATUS_A_BLUE
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    },
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    'ISO Visual': ISO_VISUAL
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}
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def select_density_standard(application, color_channel=None):
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    """
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    Select appropriate density standard for application.
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    Parameters:
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    - application: 'printing', 'photography', 'visual'
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    - color_channel: 'red', 'green', 'blue' (if applicable)
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    Returns:
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    Appropriate density standard
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    """
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    if application == 'printing':
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        if color_channel:
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            return density_standards['Status T'][color_channel]
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        else:
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            return density_standards['Status T']['red']  # Default
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    elif application == 'photography':
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        if color_channel:
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            return density_standards['Status A'][color_channel]
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        else:
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            return density_standards['Status A']['red']  # Default
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    elif application == 'visual':
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        return density_standards['ISO Visual']
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    else:
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        raise ValueError(f"Unknown application: {application}")
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# Example usage
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printing_red_standard = select_density_standard('printing', 'red')
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visual_standard = select_density_standard('visual')
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```
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### Chromatic Adaptation Matrices
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```python
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from colormath.color_constants import ADAPTATION_MATRICES
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from colormath.chromatic_adaptation import apply_chromatic_adaptation
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# Available adaptation methods
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adaptation_methods = list(ADAPTATION_MATRICES.keys())
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print(f"Available adaptation methods: {adaptation_methods}")
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# Get Bradford adaptation matrix
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bradford_matrix = ADAPTATION_MATRICES['bradford']['M']
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bradford_inverse = ADAPTATION_MATRICES['bradford']['M_inv']
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# Apply chromatic adaptation
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xyz_adapted = apply_chromatic_adaptation(
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    val_x=0.4, val_y=0.3, val_z=0.2,
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    orig_illum='d65',
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    targ_illum='d50', 
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    adaptation='bradford'
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)
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```
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### Complete Constants Inspection
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```python
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from colormath import color_constants, density_standards, spectral_constants
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def inspect_colormath_constants():
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    """Inspect all available constants in colormath."""
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    print("=== COLOR CONSTANTS ===")
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    print(f"CIE_E: {color_constants.CIE_E}")
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    print(f"CIE_K: {color_constants.CIE_K}")
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    print(f"Available observers: {color_constants.OBSERVERS}")
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    print(f"Available illuminants: {list(color_constants.ILLUMINANTS['2'].keys())}")
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    print(f"Adaptation methods: {list(color_constants.ADAPTATION_MATRICES.keys())}")
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    print("\n=== DENSITY STANDARDS ===")
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    status_t_standards = [name for name in dir(density_standards) if 'STATUS_T' in name]
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    status_a_standards = [name for name in dir(density_standards) if 'STATUS_A' in name]
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    print(f"Status T standards: {len(status_t_standards)}")
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    print(f"Status A standards: {len(status_a_standards)}")
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    print(f"Visual density threshold: {density_standards.VISUAL_DENSITY_THRESH}")
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    print("\n=== SPECTRAL CONSTANTS ===")
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    illuminants = [name for name in dir(spectral_constants) if 'REFERENCE_ILLUM' in name]
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    print(f"Reference illuminants: {len(illuminants)}")
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    return {
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        'color_constants': len([attr for attr in dir(color_constants) if not attr.startswith('_')]),
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        'density_standards': len([attr for attr in dir(density_standards) if not attr.startswith('_')]),
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        'spectral_constants': len([attr for attr in dir(spectral_constants) if not attr.startswith('_')])
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    }
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# Inspect all constants
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constants_summary = inspect_colormath_constants()
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```
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## Standard Illuminant Specifications
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### Common Illuminants
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| Illuminant | Description | Color Temperature | Applications |
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|------------|-------------|-------------------|-------------|
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| A | Tungsten incandescent | 2856K | Photography, general lighting |
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| B | Direct sunlight | 4874K | Obsolete, historical reference |
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| C | Average daylight | 6774K | Photography, obsolete |
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| D50 | Daylight | 5003K | Graphic arts, printing |
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| D55 | Daylight | 5503K | Photography |
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| D65 | Daylight | 6504K | Video, computer displays |
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| D75 | Daylight | 7504K | LCD backlighting |
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| E | Equal energy | N/A | Theoretical reference |
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### Observer Angles
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| Observer | Description | Field of View | Applications |
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|----------|-------------|---------------|-------------|
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| 2° | CIE 1931 Standard Observer | 2° field | Small samples, historical |
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| 10° | CIE 1964 Supplementary Observer | 10° field | Large samples, modern standard |
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## Density Standards Applications
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### Status T (Transmission)
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- Color negative film processing
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- Transmission densitometry
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- Color reproduction evaluation
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### Status A (Reflection)  
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- Print density measurement
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- Paper and ink evaluation
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- Quality control in printing
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### Status E (Photographic)
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- Black and white photography
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- Photographic printing
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- Film density evaluation
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### Status M (Motion Picture)
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- Cinema film processing
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- Motion picture printing
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- Theater projection standards
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### ISO Visual
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- Visual color assessment
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- Human vision correlation
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- Perceptual color evaluation