Hundreds of spectral bands reveal material composition and biochemical properties
2026-02-27
In the late 1990s, NASA’s Jet Propulsion Laboratory began flying the AVIRIS spectrometer over the Cuprite mining district of Nevada — a classic hydrothermal alteration zone with exposures of alunite, kaolinite, buddingtonite, and other minerals that are spectroscopically distinctive but visually similar. The 224-band images produced by AVIRIS, covering wavelengths from 400 to 2500 nm in 10 nm increments, could distinguish these minerals from aircraft altitude as clearly as a field geologist with a spectrometer could distinguish them in hand sample. Exploration geologists took note. Within a decade, hyperspectral survey had become a standard tool for regional mineral mapping, capable of covering thousands of square kilometres in a few days at a fraction of the cost of ground survey.
A standard satellite or aircraft sensor might capture 4 to 12 spectral bands. Hyperspectral imaging captures 100 to 400 narrow bands, sampling reflected sunlight essentially continuously from the visible through the shortwave infrared. The result is not a colour image but a spectrum for every pixel — a spectral fingerprint that encodes the chemical composition of the surface. Different minerals have different absorption features at characteristic wavelengths: the iron oxide hematite absorbs at 490 nm; kaolinite shows absorption doublets at 1400 and 2200 nm; water absorbs at 1400 and 1900 nm. These features can be identified by comparing pixel spectra to reference libraries, or extracted using spectral unmixing — the algebraic decomposition of each pixel spectrum into fractional contributions from end-member spectra. This model derives the spectral signature physics, implements absorption feature analysis, and shows how linear unmixing maps sub-pixel composition across a scene.
Can we identify minerals from orbit using reflected sunlight?
Hyperspectral imaging captures continuous spectra across hundreds of narrow bands.
Comparison:
Multispectral (Landsat, Sentinel-2): - 8-12 broad bands - Band width: 50-200 nm - Coarse spectral sampling
Hyperspectral (AVIRIS, EnMAP, PRISMA): - 100-400+ narrow bands - Band width: 5-10 nm - Fine spectral sampling - Continuous spectrum 400-2500 nm
Key advantage:
Narrow bands capture diagnostic absorption features that reveal: - Mineral composition (geology) - Vegetation biochemistry (chlorophyll, water, nitrogen) - Water quality (sediment, algae, dissolved organic matter) - Urban materials (roof types, pavement)
Applications: - Mineral exploration (ore deposits) - Precision agriculture (crop health, nutrient status) - Environmental monitoring (water quality, invasive species) - Geological mapping (lithology discrimination)
Reflectance spectrum:
\rho(\lambda) = \frac{L_{\uparrow}(\lambda)}{L_{\downarrow}(\lambda)}
Where: - \rho(\lambda) = spectral reflectance (0-1) - \lambda = wavelength (nm) - L_{\uparrow} = upwelling radiance - L_{\downarrow} = downwelling irradiance
Absorption features:
Materials absorb specific wavelengths due to: - Electronic transitions (UV-visible, 400-700 nm) - Vibrational overtones (near-infrared, 700-1300 nm) - Molecular vibrations (shortwave infrared, 1300-2500 nm)
Example - vegetation: - 680 nm: Chlorophyll absorption (red) - 750-900 nm: High reflectance (near-infrared plateau) - 1400, 1900 nm: Water absorption - 2200 nm: Cellulose/lignin absorption
Example - minerals: - Iron oxides: Absorption 400-700 nm - Hydroxyl minerals (clays): 1400, 2200 nm - Carbonates: 2300-2350 nm
Reference spectra measured in laboratory:
USGS Spectral Library: - 1400+ materials - Minerals, rocks, soils - Vegetation, water - Measured at high resolution
Use: Compare image spectra to library for identification
Data structure:
Hyperspectral cube: - x dimension: spatial (pixels across) - y dimension: spatial (pixels down) - z dimension: spectral (wavelengths)
Data volume:
1000 × 1000 pixels × 200 bands = 200 million values
Each pixel = complete spectrum (hundreds of measurements)
Mixed pixel problem:
Pixel contains multiple materials (vegetation + soil, multiple minerals)
Linear mixing model:
\rho(\lambda) = \sum_{i=1}^{n} f_i \rho_i(\lambda) + \varepsilon(\lambda)
Where: - f_i = fractional abundance of endmember i - \rho_i(\lambda) = reflectance spectrum of pure endmember i - \varepsilon(\lambda) = residual error
Constraints:
\sum_{i=1}^{n} f_i = 1 (fractions sum to 1)
f_i \geq 0 (non-negative fractions)
Matrix formulation:
\mathbf{r} = \mathbf{E} \mathbf{f} + \boldsymbol{\varepsilon}
Where: - \mathbf{r} = measured spectrum (m × 1 vector, m bands) - \mathbf{E} = endmember matrix (m × n, n endmembers) - \mathbf{f} = abundance vector (n × 1)
Solution (least squares):
\mathbf{f} = (\mathbf{E}^T\mathbf{E})^{-1}\mathbf{E}^T\mathbf{r}
Subject to non-negativity and sum-to-one constraints.
Continuum removal:
Continuum-removed reflectance:
R_{CR}(\lambda) = \frac{\rho(\lambda)}{\rho_{continuum}(\lambda)}
Absorption depth:
D = 1 - \min(R_{CR}(\lambda))
Example - 2200 nm clay feature:
If minimum R_{CR} = 0.75, then D = 0.25 (25% absorption)
Similarity metric between spectra:
\alpha = \arccos\left(\frac{\mathbf{r}_1 \cdot \mathbf{r}_2}{||\mathbf{r}_1|| \cdot ||\mathbf{r}_2||}\right)
Where: - \alpha = spectral angle (radians or degrees) - Small angle → similar spectra
Classification:
Compare pixel spectrum to reference library spectra, assign to closest match (smallest angle).
Insensitive to illumination (brightness variations) - measures shape, not magnitude.
Dimensionality reduction:
Transform 200 bands → 5-10 principal components capturing most variance.
Covariance matrix:
\mathbf{C} = \frac{1}{n-1}\mathbf{X}^T\mathbf{X}
Eigenvalue decomposition:
\mathbf{C}\mathbf{v}_i = \lambda_i\mathbf{v}_i
Principal components:
PC_i = \mathbf{X}\mathbf{v}_i
Variance explained:
\text{Variance}_i = \frac{\lambda_i}{\sum \lambda_i}
First few PCs typically capture >95% variance.
Problem: Unmix pixel containing vegetation and soil.
Measured spectrum (simplified, 5 wavelengths):
| λ (nm) | ρ_measured |
|---|---|
| 550 | 0.08 |
| 670 | 0.06 |
| 800 | 0.35 |
| 1600 | 0.25 |
| 2200 | 0.22 |
Endmember spectra:
Vegetation:
| λ (nm) | ρ_veg |
|---|---|
| 550 | 0.10 |
| 670 | 0.04 |
| 800 | 0.50 |
| 1600 | 0.35 |
| 2200 | 0.30 |
Soil:
| λ (nm) | ρ_soil |
|---|---|
| 550 | 0.06 |
| 670 | 0.08 |
| 800 | 0.20 |
| 1600 | 0.15 |
| 2200 | 0.14 |
Find fractional abundances f_{\text{veg}} and f_{\text{soil}}.
Linear mixing model:
\rho(\lambda) = f_{\text{veg}} \rho_{\text{veg}}(\lambda) + f_{\text{soil}} \rho_{\text{soil}}(\lambda)
With constraint: f_{\text{veg}} + f_{\text{soil}} = 1
Substitute constraint: f_{\text{soil}} = 1 - f_{\text{veg}}
\rho(\lambda) = f_{\text{veg}} \rho_{\text{veg}}(\lambda) + (1-f_{\text{veg}}) \rho_{\text{soil}}(\lambda)
\rho(\lambda) = f_{\text{veg}} (\rho_{\text{veg}}(\lambda) - \rho_{\text{soil}}(\lambda)) + \rho_{\text{soil}}(\lambda)
Solve using one wavelength (800 nm):
$0.35 = f_{\text{veg}}(0.50 - 0.20) + 0.20$
$0.35 = 0.30 f_{\text{veg}} + 0.20$
$0.15 = 0.30 f_{\text{veg}}$
f_{\text{veg}} = 0.50
f_{\text{soil}} = 0.50
Verify at 670 nm:
\rho_{pred} = 0.50(0.04) + 0.50(0.08) = 0.02 + 0.04 = 0.06 ✓
Verify at 2200 nm:
\rho_{pred} = 0.50(0.30) + 0.50(0.14) = 0.15 + 0.07 = 0.22 ✓
Result: Pixel is 50% vegetation, 50% soil.
Note: Using all bands simultaneously with least squares gives more robust estimate.
Below is an interactive hyperspectral analysis tool.
<label>
Vegetation fraction:
<input type="range" id="veg-frac" min="0" max="100" step="5" value="50">
<span id="veg-val">50</span>%
</label>
<label>
Add noise:
<input type="checkbox" id="add-noise">
</label>
<label>
Show endmembers:
<input type="checkbox" id="show-endmembers" checked>
</label>
<label>
Analysis method:
<select id="analysis-method">
<option value="mixture">Linear unmixing</option>
<option value="sam">Spectral Angle Mapper</option>
<option value="absorption">Absorption features</option>
</select>
</label>
<div class="hyper-info">
<p><strong>Estimated vegetation:</strong> <span id="est-veg">--</span>%</p>
<p><strong>Estimated soil:</strong> <span id="est-soil">--</span>%</p>
<p><strong>RMSE:</strong> <span id="rmse">--</span></p>
<p><strong>Classification:</strong> <span id="classification">--</span></p>
</div><canvas id="hyper-canvas" width="700" height="400" style="border: 1px solid #ddd;"></canvas>Observations: - Green dashed line shows pure vegetation spectrum with strong NIR reflectance - Brown dashed line shows pure soil spectrum with more uniform response - Blue line with points is measured mixed spectrum - Pink dotted line is reconstructed spectrum from unmixing - Red marker at 670 nm shows chlorophyll absorption feature - Green marker at 850 nm shows NIR plateau characteristic of vegetation - Unmixing algorithm estimates component fractions from spectral shape - Adding noise degrades unmixing accuracy but algorithm remains robust - RMSE quantifies reconstruction quality
Key insights: - Vegetation has distinctive spectral signature with red absorption and NIR reflectance - Mixed pixels can be decomposed into constituent materials - Narrow bands enable precise absorption feature measurement - Spectral libraries provide reference signatures for identification
Example - Cuprite, Nevada mining district:
AVIRIS hyperspectral data identified: - Kaolinite (2200 nm absorption) - Alunite (2165 nm absorption) - Buddingtonite (2125 nm absorption) - Iron oxides (500-600 nm absorption)
Economic value:
Mapping alteration minerals indicates hydrothermal systems associated with ore deposits.
Advantage over field mapping:
Crop biochemistry from spectra:
Chlorophyll content: - Red edge position (700-750 nm) - Chlorophyll indices using 550, 670, 750 nm
Water stress: - Water absorption at 1400, 1900 nm - Normalized difference water index
Nitrogen status: - Correlation with chlorophyll - Red edge shifts with N availability
Disease detection: - Early stress signatures before visual symptoms - Spectral changes in stressed tissue
Application:
Variable-rate fertilizer/pesticide application based on hyperspectral maps.
Optically active constituents:
Chlorophyll-a (algae): - Absorption at 440, 675 nm - Fluorescence peak at 685 nm
Suspended sediment: - Scattering increases reflectance across all bands - Particularly strong in red/NIR
Dissolved organic matter (DOM): - Absorption in blue/green - “Yellow substance”
Example - Lake Erie harmful algal blooms:
Hyperspectral imaging from aircraft detects: - Bloom extent - Chlorophyll concentration - Cyanobacteria vs green algae discrimination
Public health application:
Toxic cyanobacteria produce microcystin - early detection enables beach closures.
Problem:
Atmosphere absorbs and scatters light.
Water vapor absorption bands: - 1400 nm - 1900 nm - 2500+ nm
In these bands: Surface reflectance unmeasurable from aircraft/satellite.
Solution: - Atmospheric correction (ATREM, FLAASH algorithms) - Use bands outside absorption features - Ground-based measurements for validation
Assumption: Pure endmembers have fixed spectra.
Reality: - Vegetation spectra vary with species, health, phenology - Soil spectra vary with moisture, texture, mineralogy - Shadows, topography affect apparent spectra
Problem:
Using library spectra from different location/time introduces error.
Solution: - Image-derived endmembers (select from actual scene) - Multiple endmember spectral mixture analysis (MESMA) - Account for variability in library
High dimensionality (200+ bands) causes statistical problems:
Hughes phenomenon: - Classification accuracy decreases with too many features - Need exponentially more training samples
Multicollinearity: - Adjacent bands highly correlated - Redundant information
Solution: - Dimensionality reduction (PCA, MNF) - Band selection (choose optimal subset) - Feature extraction (spectral indices)
Linear model assumes:
Photons interact with one material before sensor.
Reality - multiple scattering: - Canopy: Photons bounce between leaves, soil - Mineral mixtures: Intimate vs areal mixing behave differently
Non-linear effects especially strong in: - Dense vegetation - Rough surfaces - Multiple scattering media
Solution: - Non-linear unmixing models - Radiative transfer modelling - Acknowledge limitation in interpretation
Spectral derivatives enhance subtle features.
First derivative:
\frac{d\rho}{d\lambda} \approx \frac{\rho(\lambda_{i+1}) - \rho(\lambda_{i-1})}{2\Delta\lambda}
Second derivative:
\frac{d^2\rho}{d\lambda^2} \approx \frac{\rho(\lambda_{i+1}) - 2\rho(\lambda_i) + \rho(\lambda_{i-1})}{\Delta\lambda^2}
Advantages: - Remove background (continuum) - Enhance narrow absorption features - Less sensitive to illumination variations
Red edge derivative:
First derivative peak position indicates chlorophyll content and plant stress.
Mineral identification:
Second derivative reveals overlapping absorption features invisible in original spectrum.
Challenge:
Derivatives amplify noise - require smoothing.
Definition:
\mathbf{a} \cdot \mathbf{b} = \sum_{i=1}^{n} a_i b_i = ||\mathbf{a}|| \cdot ||\mathbf{b}|| \cos\theta
Where \theta = angle between vectors.
Normalized dot product:
\text{similarity} = \frac{\mathbf{a} \cdot \mathbf{b}}{||\mathbf{a}|| \cdot ||\mathbf{b}||} = \cos\theta
Range: -1 to +1 - +1: Identical direction - 0: Orthogonal - -1: Opposite direction
Spectral Angle Mapper uses this:
Angle \alpha = \arccos(\text{similarity})
Small angle → high similarity
d = ||\mathbf{a} - \mathbf{b}|| = \sqrt{\sum_{i=1}^{n} (a_i - b_i)^2}
Sensitive to magnitude - bright and dark versions of same material have large distance.
Spectral angle insensitive to magnitude - better for reflectance spectra.