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References

Helia implements published methods. This page lists them, with the place in the code that uses each. The same citations are in the doc comments of the modules, under a # References heading. Where the code only matches the documented behaviour of another program, the page says so and no code from that program was used.

A DOI was checked against Crossref (and the arXiv listing for SOLARNET) when this page was written. Books were checked against publisher and library catalogue records, and the DCT energy ratio source against the reference list of Popowicz et al. An entry marked to verify has a detail that could not be confirmed from a primary source; treat it as a pointer, not a citation, until it is checked. At the last check (October 2026) no entry carries that marker. Corrections are welcome: use Feedback.

Lucky imaging and seeing

  • Fried, D. L. (1966). Optical resolution through a randomly inhomogeneous medium for very long and very short exposures. J. Opt. Soc. Am. 56, 1372-1379. doi:10.1364/JOSA.56.001372. The Fried parameter r0. Used by Seeing estimation.
  • Fried, D. L. (1978). Probability of getting a lucky short-exposure image through turbulence. J. Opt. Soc. Am. 68, 1651-1658. doi:10.1364/JOSA.68.001651. Why keeping only the sharpest frames works. Used by frame scoring and selection (quality).
  • Law, N. M., Mackay, C. D., Baldwin, J. E. (2006). Lucky imaging: high angular resolution imaging in the visible from the ground. Astron. Astrophys. 446, 739-745. doi:10.1051/0004-6361:20053695.
  • von der Luehe, O. (1984). Estimating Fried's parameter from a time series of an arbitrary resolved object. J. Opt. Soc. Am. A 1, 510-519. doi:10.1364/josaa.1.000510. The spectral ratio (seeing::spectral).
  • Scharmer, G. B., van Werkhoven, T. I. M. (2010). S-DIMM+ height characterization of day-time seeing using solar granulation. Astron. Astrophys. 513, A25. doi:10.1051/0004-6361/200913791. The alignment point motion index (seeing::motion).
  • Noll, R. J. (1976). Zernike polynomials and atmospheric turbulence. J. Opt. Soc. Am. 66, 207-211. doi:10.1364/JOSA.66.000207. The Kolmogorov phase spectrum of the test screens.
  • Lane, R. G., Glindemann, A., Dainty, J. C. (1992). Simulation of a Kolmogorov phase screen. Waves in Random Media 2, 209-224. doi:10.1088/0959-7174/2/3/003. FFT phase screens with subharmonics (seeing::screen).

Registration, resampling and mosaics

  • Kuglin, C. D., Hines, D. C. (1975). The phase correlation image alignment method. Proc. IEEE Int. Conf. on Cybernetics and Society, 163-165. To verify (no DOI; page range from memory). Global alignment (align::global).
  • Cooley, J. W., Tukey, J. W. (1965). An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 297-301. doi:10.2307/2003354. The mixed-radix FFT in the GPU registration kernels.
  • Harris, F. J. (1978). On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66, 51-83. doi:10.1109/PROC.1978.10837. The Hann window.
  • Beaton, A. E., Tukey, J. W. (1974). The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data. Technometrics 16, 147-185. doi:10.1080/00401706.1974.10489171. The biweight of the limb fit (align::limb).
  • Duchon, C. E. (1979). Lanczos filtering in one and two dimensions. J. Appl. Meteorol. 18, 1016-1022. doi:10.1175/1520-0450(1979)018<1016:LFIOAT>2.0.CO;2. The Lanczos resampling kernel.
  • Padfield, D. (2012). Masked object registration in the Fourier domain. IEEE Trans. Image Process. 21, 2706-2718. doi:10.1109/TIP.2011.2181402. Mosaic panel search (mosaic::pair).
  • Lucas, B. D., Kanade, T. (1981). An iterative image registration technique with an application to stereo vision. Proc. 7th Int. Joint Conf. on Artificial Intelligence, 674-679. No DOI. Mosaic panel refinement.
  • Avidan, S., Shamir, A. (2007). Seam carving for content-aware image resizing. ACM Trans. Graph. 26(3), 10. doi:10.1145/1276377.1276390. The least-difference seam of a mosaic (mosaic::blend).
  • Fruchter, A. S., Hook, R. N. (2002). Drizzle: a method for the linear reconstruction of undersampled images. Publ. Astron. Soc. Pac. 114, 144-152. doi:10.1086/338393. The drizzle deposit; the interface exists and the method is not implemented yet.

Statistics and robust estimation

  • Huber, P. J. (1964). Robust estimation of a location parameter. Ann. Math. Statist. 35, 73-101. doi:10.1214/aoms/1177703732.
  • Huber, P. J., Ronchetti, E. M. (2009). Robust Statistics, 2nd ed. Wiley. doi:10.1002/9780470434697. The Huber step and winsorising in robust stacking (stack), the Huber weight in the mosaic solve and the self-calibrated flat.
  • Hampel, F. R. (1974). The influence curve and its role in robust estimation. J. Am. Stat. Assoc. 69, 383-393. doi:10.1080/01621459.1974.10482962. The median absolute deviation as a noise scale.
  • Rousseeuw, P. J., Croux, C. (1993). Alternatives to the median absolute deviation. J. Am. Stat. Assoc. 88, 1273-1283. doi:10.1080/01621459.1993.10476408.

Calibration and demosaicing

  • Kuhn, J. R., Lin, H., Loranz, D. (1991). Gain calibrating nonuniform image-array data using only the image data. Publ. Astron. Soc. Pac. 103, 1097-1108. doi:10.1086/132932. Self-calibrated flats (calibrate::selfflat).
  • Malvar, H. S., He, L.-W., Cutler, R. (2004). High-quality linear interpolation for demosaicing of Bayer-patterned color images. Proc. IEEE ICASSP 2004, vol. 3, iii-485. doi:10.1109/ICASSP.2004.1326587. The mhc demosaicing.

Sharpening and deconvolution

  • Holschneider, M., Kronland-Martinet, R., Morlet, J., Tchamitchian, P. (1989). A real-time algorithm for signal analysis with the help of the wavelet transform. In Wavelets: Time-Frequency Methods and Phase Space, Springer, 286-297. doi:10.1007/978-3-642-75988-8_28. The a-trous ("with holes") algorithm.
  • Starck, J.-L., Murtagh, F., Bijaoui, A. (1994). Image restoration with noise suppression using a wavelet transform and a multiresolution support constraint. Proc. SPIE 2302, 132-143. doi:10.1117/12.188035. Wavelet layers with a noise threshold per layer. (Starck and Murtagh's earlier article, "Image restoration with noise suppression using the wavelet transform", is Astron. Astrophys. 288, 342 (1994), bibcode 1994A&A...288..342S; it has no DOI and Helia cites the SPIE paper, which has one.)
  • Starck, J.-L., Murtagh, F., Bijaoui, A. (1998). Image Processing and Data Analysis: The Multiscale Approach. Cambridge University Press. ISBN 0-521-59084-1 (hardback; 978-0-521-59084-6) and 0-521-59914-8 (paperback; 978-0-521-59914-6). doi:10.1017/CBO9780511564352. The textbook treatment of the a-trous transform with the B3 spline.
  • Donoho, D. L. (1995). De-noising by soft-thresholding. IEEE Trans. Inf. Theory 41, 613-627. doi:10.1109/18.382009.
  • Richardson, W. H. (1972). Bayesian-based iterative method of image restoration. J. Opt. Soc. Am. 62, 55-59. doi:10.1364/JOSA.62.000055.
  • Lucy, L. B. (1974). An iterative technique for the rectification of observed distributions. Astron. J. 79, 745. doi:10.1086/111605.
  • Dey, N., Blanc-Feraud, L., Zimmer, C., Roux, P., Kam, Z., Olivo-Marin, J.-C., Zerubia, J. (2006). Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution. Microsc. Res. Tech. 69, 260-266. doi:10.1002/jemt.20294. Deconvolution (edit::deconv).
  • Lupton, R., Blanton, M. R., Fekete, G., Hogg, D. W., O'Mullane, W., Szalay, A., Wherry, N. (2004). Preparing red-green-blue images from CCD data. Publ. Astron. Soc. Pac. 116, 133-137. doi:10.1086/382245. The asinh stretch of the prominence layer.

Frame quality metrics

  • Popowicz, A., Radlak, K., Bernacki, K., Orlov, V. (2017). Review of image quality measures for solar imaging. Solar Phys. 292, 187. doi:10.1007/s11207-017-1211-3.
  • Helmli, F. S., Scherer, S. (2001). Adaptive shape from focus with an error estimation in light microscopy. Proc. 2nd Int. Symp. on Image and Signal Processing and Analysis (ISPA 2001), 188-193. doi:10.1109/ISPA.2001.938626. The Helmli-Scherer measure (quality_extra).
  • Shen, C.-H., Chen, H. H. (2006). Robust focus measure for low-contrast images. 2006 Digest of Technical Papers, Int. Conf. on Consumer Electronics (ICCE), 69-70. doi:10.1109/ICCE.2006.1598314. The DCT energy ratio, as named and evaluated by Popowicz et al. (2017). Helia follows Popowicz et al.'s description of it; the earlier text of this page named "Su et al.", which was wrong. The gradient-energy and Laplacian-variance metrics are textbook measures with no single source.

The Sun

  • Meeus, J. (1998). Astronomical Algorithms, 2nd ed. Willmann-Bell, Richmond, Virginia. ISBN 0-943396-61-1 (978-0-943396-61-3). Chapter 14 (parallactic angle, field rotation), chapters 25 and 29 (the Sun's position, P, B0, L0).
  • Thompson, W. T. (2006). Coordinate systems for solar image data. Astron. Astrophys. 449, 791-803. doi:10.1051/0004-6361:20054262.
  • Neckel, H., Labs, D. (1994). Solar limb darkening 1986-1990 (lambda 303 to 1099 nm). Solar Phys. 153, 91-114. doi:10.1007/BF00712494.
  • Cox, A. N. (ed.) (2000). Allen's Astrophysical Quantities, 4th ed. Springer and AIP Press, New York, ISBN 0-387-98746-0; Springer's online edition is doi:10.1007/978-1-4612-1186-0 (softcover ISBN 978-1-4612-7037-9). The quadratic limb-darkening law.
  • Howard, R. F., Harvey, J. W., Forgach, S. (1990). Solar surface velocity fields determined from small magnetic features. Solar Phys. 130, 295-311. doi:10.1007/BF00156795.
  • Snodgrass, H. B., Ulrich, R. K. (1990). Rotation of Doppler features in the solar photosphere. Astrophys. J. 351, 309. doi:10.1086/168467.
  • Howard, R. (1984). Solar rotation. Annu. Rev. Astron. Astrophys. 22, 131-155. doi:10.1146/annurev.aa.22.090184.001023. Differential rotation (derotate).
  • Clette, F., Svalgaard, L., Vaquero, J. M., Cliver, E. W. (2014). Revisiting the sunspot number. Space Sci. Rev. 186, 35-103. doi:10.1007/s11214-014-0074-2. The relative sunspot (Wolf) number R = k (10 g + s).

File formats and metadata

  • Pence, W. D., Chiappetti, L., Page, C. G., Shaw, R. A., Stobie, E. (2010). Definition of the Flexible Image Transport System (FITS), version 3.0. Astron. Astrophys. 524, A42. doi:10.1051/0004-6361/201015362. The block layout, header cards, BITPIX, BZERO/BSCALE scaling, image extensions and the bottom-row-first order that helia stack follows when it reads FITS frames (io::fits, io::fitsseq). BAYERPAT and ROWORDER are not in the standard; they are the convention of capture programs, described in the file-format page of the Siril manual (ROWORDER, BOTTOM-UP or TOP-DOWN; documentation only, no code is taken from it) and in Stack FITS frames.
  • Greisen, E. W., Calabretta, M. R. (2002). Representations of world coordinates in FITS. Astron. Astrophys. 395, 1061-1075. doi:10.1051/0004-6361:20021326.
  • Calabretta, M. R., Greisen, E. W. (2002). Representations of celestial coordinates in FITS. Astron. Astrophys. 395, 1077-1122. doi:10.1051/0004-6361:20021327.
  • SOLARNET metadata recommendations for solar observations (Haugan, Fredvik and co-authors), arXiv:2011.12139.
  • Hahn, G. SER file format. Cited in the research review; the specification is on the author's web page.

Plugins and interchange

  • JSON-RPC Working Group (2013). JSON-RPC 2.0 Specification. jsonrpc.org/specification. The message format between Helia and a plugin (helia-plugin, helia-plugin-sdk::wire). A standards document with no DOI.
  • Bray, T. (ed.) (2017). The JavaScript Object Notation (JSON) Data Interchange Format. RFC 8259. doi:10.17487/RFC8259. The text of every message.
  • Preston-Werner, T., Gedam, P. et al. (2021). TOML v1.0.0. toml.io/en/v1.0.0. The format of plugin.toml. A standards document with no DOI.
  • Wright, A., Andrews, H., Hutton, B., Dennis, G. (2022). JSON Schema: A Media Type for Describing JSON Documents (draft 2020-12). json-schema.org. The subset behind the settings form and the step parameters of a plugin (helia-plugin::schema).
  • National Institute of Standards and Technology (2015). Secure Hash Standard (SHS). FIPS PUB 180-4. doi:10.6028/NIST.FIPS.180-4. SHA-256, the checksum a plugin is approved by.
  • Josefsson, S., Liusvaara, I. (2017). Edwards-Curve Digital Signature Algorithm (EdDSA). RFC 8032. doi:10.17487/RFC8032. The key type named in the [update] section of a manifest; Helia does not verify signatures in API version 1.
  • LLVM Project. libFuzzer: a library for coverage-guided fuzz testing. llvm.org/docs/LibFuzzer.html. The fuzzing engine behind the plugin_protocol target. Project documentation with no DOI.

Behaviour matched from documentation (no code used)

Helia's wavelet controls follow the documented behaviour and value ranges of RegiStax 6, taken from the author's published pages and from the tutorials listed in Coming from RegiStax. RegiStax is closed source and no code, binary or private information was used. The prominence layer reads in the spirit of the separate disc and prominence adjustments that tools such as ImPPG offer; ImPPG's public README was read to learn what users expect, and none of its code was read or used. The research reviews under Research compare Helia with other programs from their public documentation.

See also Credits, licences and trademarks.