Hanle Echelle Spectrograph (HESP)

• HESP is a high-resolution, dual fibre-fed echelle spectrograph on the 2 m HCT at IAO, enabling precision astrophysical measurements with broad spectral coverage.
• It utilizes advanced hardware like stabilized Fabry–Perot etalons and tight environmental controls to achieve subpixel accuracy in wavelength calibration.
• Automated calibration algorithms and robust data reduction techniques empower detailed studies in radial velocity, chemical abundances, and exoplanet atmospheres.

The Hanle Echelle Spectrograph (HESP) is a high-resolution, dual fibre-fed, cross-dispersed echelle spectrograph installed on the 2 m Himalayan Chandra Telescope (HCT) at the Indian Astronomical Observatory (IAO), Hanle, India. Designed for astrophysical applications ranging from precision radial velocity measurements and chemical abundance studies to time-domain and planetary science, HESP features a broad spectral coverage (typically 3600–10,800 Å), multiple observing modes (R ≈ 30,000–60,000), and modular architectures for calibration and control. The instrument leverages both hardware innovations—such as stabilized Fabry–Perot etalons and environmental management—and advanced calibration and data reduction software, with modeling and empirical performance now validated across diverse science cases.

1. Instrument Design and Technical Capabilities

HESP utilizes a bench-mounted, cross-dispersed echelle design with dual fibre inputs (standard and reference), ensuring both high throughput and simultaneous source/calibration capability (Aravind et al., 3 Mar 2024). The spectrograph operates in medium-resolution (R ≈ 30,000 via 2.7″ fibre) and high-resolution (R ≈ 60,000 via image slicer) modes. Key components include:

• Slit assembly and fibre feeds, optimized for both sky and calibration sources.
• Collimator and echelle grating dispersing light into multiple diffraction orders.
• Cross-disperser prisms and a multi-element camera for order separation and focusing.
• A large-format CCD detector capturing 2D echellograms spanning 3700–10,800 Å in a single exposure (&&&1&&&, Aravind et al., 3 Mar 2024).

Environmental sensitivity is mitigated by tight temperature and pressure regulation. For highest calibration precision, vacuum enclosures and digital controllers stabilize key elements, and specialized optical mounts maintain alignment. The instrument supports insertion of calibration sources (Th–Ar, Fabry–Perot etalon) and employs broadband coatings (500–750 nm) on critical surfaces (Das et al., 2020).

2. Calibration Methodologies and Modeling

HESP’s wavelength calibration employs a physics-based modeling scheme that predicts line centroids with subpixel accuracy, eschewing commercial ray tracing software in favor of modular, analytic techniques (Chanumolu et al., 2015). The modeling workflow:

• Chains paraxial ray traces of all major optical components (slit, collimator, grating, prisms, camera, detector).
• Applies exact surface corrections (e.g. collimator sag):

$$dz = \frac{c_x x^2 + c_y y^2}{1 + \sqrt{1 - (1 + k_x)c_x^2x^2 - (1 + k_y)c_y^2y^2}}$$

• Expands camera system aberrations using Buchdahl coefficients in homogeneous polynomials (3rd, 5th, 7th order).
• Models glass dispersion via SeLLMeier relations:

$$n^2 - 1 = \frac{A_1 \lambda^2}{\lambda^2 - B_1} + \frac{A_2 \lambda^2}{\lambda^2 - B_2} + \frac{A_3 \lambda^2}{\lambda^2 - B_3}$$

Calibration is performed using ThAr lamp exposures, extracting 1D Gaussian centroids on both dispersion axes. Simulated annealing optimizes key “open” parameters such as slit–mirror distances, tilts, grating/prism angles, camera ABCD, and CCD alignments, minimizing a weighted RMS merit function:

$$M = \sqrt{\frac{1}{N} \sum_{i=1}^{N} w_i (\mathbf{p}_i^{meas} - \mathbf{p}_i^{model})^2}$$

Monte Carlo simulations quantify photon noise impacts, with matching achieved at ~0.08 pixel precision. The model predictions align to within 10⁻⁵ mm of commercial ray tracing software when aberration terms are properly included (Chanumolu et al., 2015, Chanumolu et al., 2017).

3. Advanced and Automatic Calibration Algorithms

Automatic calibration algorithms, such as those implemented in the open-source xwavecal Python package (Brandt et al., 2019), introduce further automation and robustness. The approach:

• Exploits duplicates of spectral features in overlapping echelle orders to constrain the scale-invariant component of the wavelength solution:

$$\lambda(x, i) = \frac{K}{m_0 + i}\left[1 + \sum_{q=0}^{2}\sum_{c=1}^{2} b_{qc} P_q(i) P_c(x) \right]$$

• Solves for transformation functions $g_i(x)$ such that

$\lambda(x, i+1) = \lambda(g_i(x), i)$

• Anchors global scale $K$ by matching measured line centers to laboratory wavelengths, searching and refining $K$ via IRWLS and optimization.
• Achieves velocity precision of 1–10 m/s on HARPS and NRES, with expected applicability to HESP. The xwavecal package supports configuration-driven and modular operation, yielding calibrated spectra in less than 30 s per exposure on single cores.

4. Calibration Hardware: Fabry–Perot Etalon Developments

For precision Doppler work, HESP incorporates a passively stabilized Fabry–Perot etalon calibrator (Das et al., 2020):

• The FP etalon consists of two broadband-coated fused silica mirrors separated by Zerodur spacers, housed within a stainless-steel vacuum enclosure (<1 mbar).
• Precise thermal control (±0.05 °C) is achieved via Arduino-driven digital PI loops.
• The FP delivers a dense, uniform “comb” of calibration lines (FSR ≈ 30 GHz), with initial tests showing 6124 lines across 24 orders (500–750 nm), supporting a velocity precision of 1–10 m/s.
• The transmission function:

$I_T = \frac{I_0}{1 + F \sin^2(\delta/2)}$

Table: Key Technical Specifications (from (Das et al., 2020))

Parameter	Value	Note
Cavity Thickness	5 mm ±0.001	Zerodur spacers, Fused Silica mirrors
Clear Aperture	20 mm	Optical fibre overfill
FSR	30 GHz	500–750 nm calibration band
Coating Reflectivity	~60%	Broadband (500–750 nm)

5. Post-Processing and Data Reduction

HESP datasets often exhibit curvature and tilt artifacts in spectral orders, which can compromise line centroids and calibration (Das et al., 2021):

• Curvature correction: Aperture centers traced via polynomial fits; 2D extraction aligns orders, removes curvature via spline stacking.
• Tilt correction: For each line, edge detection (Canny, mean-threshold) and centroid/slope measurement; lines are rectified by pixel remapping:

$x_s = x' - (y' - y_0) \times slope$

• Reductions in FWHM and improved finesse (e.g., from 2.167 to 2.208) validate the approach.
• These corrections are necessary for high-precision tasks, notably in instruments such as MIKE and X-shooter, but also for subtle improvements in HESP.

6. Scientific Applications and Performance Results

The instrument’s precision calibration and broad coverage support a range of astrophysical studies:

• Chemical Abundance Analysis: HESP has resolved neutron-capture element abundances (Sr, Y, Zr, Ba, Ce, Nd, Sm, Eu, Dy) in r-process-enhanced metal-poor stars (Bandyopadhyay et al., 2020), employing LTE models (ATLAS9/TURBOSPECTRUM), robust SNR, and accounting for blends/hyperfine splitting. Abundances are reported as:

$\log \epsilon(X) = \log(N_X/N_H) + 12.0$

$[X/Y] = \log(N_X/N_Y)_\star - \log(N_X/N_Y)_\odot$

• Carbon Star Characterization: High-resolution spectra allowed classification of CH giant and CEMP-r/s star types, with dilution modeling for neutron-capture patterns (Shejeelammal et al., 2021).
• Cometary Spectroscopy: HESP resolved blended vibrational and rotational bands of volatile molecules and forbidden atomic oxygen lines, analyzing green-to-red [OI] ratios and NH$_2$ ortho-to-para ratios, yielding spin temperatures (e.g., $T_{spin} \sim 26$ K for NH$_2$ in 46P) (Aravind et al., 3 Mar 2024).
• Exoplanet Atmosphere Studies: Initial HRTS on HD 209458b achieved subpercent precision in transmission residuals (Na I D lines), employing a semi-automated Python pipeline—incorporating bias/cosmic ray correction, PyRAF spectral extraction, telfit-based telluric removal, barycentric and systemic RV corrections (Bestha et al., 21 Sep 2025).

7. Impact, Future Prospects, and Science Cases

The advanced calibration schemes and robust instrumentation enable:

• Enhanced radial velocity studies of M-dwarfs or exoplanet host stars, even in regimes with sparse calibration lines (Chanumolu et al., 2017).
• Detailed abundance analysis and stellar population studies pertinent to galactic chemical evolution.
• Precision cometary composition studies, including spatially resolved coma analysis.
• Ground-based HRTS for exoplanet atmospheres with subpercent sensitivity, using moderate-sized telescopes.
• Prospects for further improvement include more stable FP calibration with smaller fibre feeds, active cavity tracking, and integration of automatic calibration routines such as xwavecal or advanced tilt corrections.
• The methodology—combining physical modeling, empirical optimization, hardware stabilization, and automated reduction—ensures traceability and reproducibility in high-precision astronomical spectroscopy (Chanumolu et al., 2015, Chanumolu et al., 2017, Brandt et al., 2019, Das et al., 2020, Bandyopadhyay et al., 2020, Das et al., 2021, Aravind et al., 3 Mar 2024, Bestha et al., 21 Sep 2025).