Using the web interface

Use the web interface to estimate the exposure time needed for a target signal-to-noise ratio, or the signal-to-noise ratio expected from a given exposure.

One calculation form brings together the observing setup, source model, photometry method, sky background, and telescope and atmospheric conditions.

Note

PyDIET is an exposure time calculator (ETC): its predictions depend on the instrument and atmosphere models. These models have been statistically validated for MegaCam and WIRCam, but the results remain estimates for planning, comparison, and feasibility studies rather than guarantees of on-sky performance.

The symbol marks features or settings specific to the supplied CFHT configuration.

Overview of the main page

The main page contains:

a top navigation bar;
a settings panel;
an instrument-specific ETC form;
links to the Terms of Service, CFHT home page, and Privacy Policy.

|PyDIET| web interface — Fig. 1 The main PyDIET web interface.

The top-right corner displays the running PyDIET version. When comparing or reporting results, record this version along with the instrument, filter, source and sky models, and observing parameters. A small disk beside the version indicates the server connection status:

green means the server is responding to health checks;
red means the server is unavailable, unreachable, or too busy to respond.

Settings

The Settings button opens the global settings panel. These settings affect the web interface and the default calculation context.

Theme

The Theme setting changes the appearance of the interface, with light, dark, and automatic modes available in the supplied client.

This option only changes the display of the page. It has no effect on the ETC model or on the calculated results.

Instrument

The PyDIET web interface can provide access to several instruments through a common page. The Instrument setting selects the instrument model and interface used by the ETC.

The current CFHT-oriented configuration includes:

MegaCam, an optical wide-field imager;
WIRCam, a near-infrared imager.

The selected instrument determines which filter list is loaded. It also selects detector parameters such as gain, readout noise, full-well capacity, pixel scale, and quantum efficiency.

The settings panel also provides links to the manual, web API documentation, and source code repository. To use the calculator from a script, follow Using the web API.

ETC form

Describe your observation using the form's controls, then press Submit. Some controls appear only when needed, such as the galaxy parameters when you select a galaxy source model.

Compute

The Compute menu selects the quantity to calculate.

Available choices are:

exposure time: enter a target signal-to-noise ratio (SNR). PyDIET estimates the exposure time required to reach it.
SNR: the signal-to-noise input field is replaced by an Exposure Time [s] field. Enter the exposure time in seconds to estimate the SNR for the selected source type.

Internally, both modes use the same noise model.

Exposures

The Exposures field sets the number of exposures in the observing sequence.

The default is one exposure; selecting more than one reveals the Stacking menu.

The number of exposures affects the total integration time and the number of readouts. Increasing the number of exposures increases the accumulated source signal and sky signal, but also increases the cumulative contribution of readout noise.

For a fixed total exposure time, splitting the observation into many short exposures is therefore not equivalent to taking fewer long exposures, especially in low-background or narrow-band regimes where read noise matters.

Stacking

The Stacking menu is shown only when Exposures is greater than one.

Available choices are:

average: PyDIET assumes that independent exposures are combined using the mean. This preserves the usual \(\sqrt{N}\) improvement in signal-to-noise ratio for \(N\) equivalent exposures, apart from additional readout-noise terms.
median: PyDIET applies a correction for the lower statistical efficiency of the median compared with the mean. For Gaussian noise, a median stack has a larger variance than an average stack.

Median stacking is more robust against cosmic rays, bad pixels, and outliers, but it is not quite as efficient as averaging when all exposures are otherwise clean. Other artifact-rejection methods can provide intermediate SNRs, so the average and median options offer useful bounds for planning.

The default is median.

Source type

The Source type menu describes the spatial distribution of the astronomical source.

Available choices are:

point source: the source is modeled as an unresolved object. Its image depends mainly on the seeing, instrumental point spread function (PSF), and detector sampling.

Use this option for stars, unresolved transients, quasars, and compact sources that are not significantly resolved by the instrument.
galaxy: the source is modeled as an extended source with a pure, axisymmetric Sérsic surface-brightness profile convolved with the full PSF. The resulting image gives a reasonably accurate description of an elliptical or (face-on) disk galaxy. It is more extended than a point source, so the source light is spread over more pixels. For the same total magnitude, this lowers the achievable SNR because more sky background contributes to the measurement.
extended: the source has a uniform profile, specified by its surface brightness per unit angular area. When this option is selected, the photometry menu is hidden and the brightness field changes to a surface brightness quantity per square arcsecond.

Use this option for diffuse emission, nebular emission, sky-like surface brightness estimates, or extended low-surface-brightness structures where the relevant quantity is flux per unit angular area.

Selecting galaxy reveals two additional Sérsic profile parameters: effective radius and index.

Sérsic Rₑ

The Sérsic Rₑ field sets the effective angular radius of the galaxy in arcseconds. This is the radius enclosing half of the intrinsic model flux before convolution with the PSF.

Larger values make the source more extended and reduce the signal-to-noise ratio for a fixed total magnitude.

Sérsic index

The Sérsic index controls the concentration of the galaxy profile.

A value near 1 corresponds approximately to an exponential disk. Larger values represent more centrally concentrated profiles, such as bulge-like or elliptical galaxy profiles.

At fixed total magnitude and effective radius, a larger Sérsic index puts more light near the center, which may improve detectability in compact apertures or model-fitting measurements, but can also make the result more sensitive to the seeing model.

Seeing

The Seeing field sets the delivered image quality in arcseconds in the selected filter. It is the angular full width at half maximum (FWHM) of the PSF, excluding the pixel footprint. The default value is 0.7 arcsec.

For point sources and galaxies, worse seeing spreads the source flux over more pixels. This increases the amount of sky background and detector noise included in the measurement, generally reducing SNR for a fixed exposure time.

Seeing does not directly change the surface brightness of a uniform extended source. See Methods for the source-model assumptions.

Filter

The Filter menu selects the filter transmission curve used in the calculation.

Changing the filter can strongly affect:

the number of detected source electrons;
the sky background;
the atmospheric extinction;
the thermal background, especially in the near infrared;
the conversion between AB magnitude, Vega magnitude, flux density, and photon (electron) counts.

The available filters depend on the selected instrument.

For MegaCam at CFHT, the current configuration includes broad-band filters such as u, g, r, i, z, gri and several narrow or medium-band filters such as CaHK, OIII, Hα, and related off-band filters.

For WIRCam, the current configuration includes near-infrared filters such as Y, J, H, Ks, H2, Low OH, CH4 on/off, K cont., Brγ, and W.

upload: if available, selecting this option opens a file input for a custom filter transmission curve. The uploaded file should be a FITS table file containing the transmission curve.

This is useful for testing new filters, provisional filters, or user-defined bandpasses without modifying the server-side instrument configuration.

Source magnitude/flux

The Source magnitude field sets the source flux.

The field label changes depending on the selected source type and source unit.

For point sources and galaxies, the value describes the total source brightness. For extended sources, it describes a surface brightness per square arcsecond.

Source unit

The Source unit menu selects how the source brightness is interpreted.

Available choices are:

AB mag: the source brightness is interpreted as an AB magnitude. For point sources and galaxies, this is the total AB magnitude of the source. For extended sources, it becomes an AB surface brightness in mag.arcsec^-2.

PyDIET converts the AB magnitude into a spectral flux density normalization and integrates it through the selected total throughput curve.
Vega mag: the source brightness is interpreted as a Vega-based magnitude. For point sources and galaxies, this is the total Vega magnitude. For extended sources, it becomes a Vega surface brightness in mag.arcsec^-2.

PyDIET converts the Vega magnitude to a physical flux using a Vega reference spectrum and the selected bandpass. The AB-Vega offset therefore depends on the filter.
μJy: the source brightness is interpreted as a flux density in microjanskys. For extended sources, this becomes μJy.arcsec^-2.

PyDIET converts the input flux density to a photon rate through the selected bandpass. This option is useful when the source flux is already known in physical units rather than as a magnitude.
flux: the source brightness is interpreted as an integrated physical flux, in units of 10^-15erg.s^-1.cm^-2 or, for extended sources, 10^-15erg.s^-1.cm^-2.arcsec^-2. This option is meant for narrow-band calculations.

PyDIET treats the value as an integrated flux over the selected bandpass. For broad-band continuum work, magnitudes or μJy are usually less ambiguous.

Photometry type

The Photometry type menu selects how the source flux is measured. It is hidden for extended sources.

Available choices are:

model-fitting: PyDIET estimates the source flux by fitting the source model to the image.

For a point source, the fitted model is the PSF. For a galaxy, it is the seeing-convolved Sérsic model.

In the idealized Gaussian white noise limit, model fitting provides an efficient flux estimator because pixels are weighted according to the expected source profile and noise variance. It usually gives the best formal SNR when the source model is accurate.
Optimal aperture: PyDIET chooses an aperture that maximizes the expected SNR for the selected source, seeing, sky background, and detector noise.

For a point source, the optimal aperture is usually a compromise: a larger aperture includes more source flux but also more sky noise. The optimum is therefore smaller than an aperture that captures nearly all the flux.

For galaxies, the optimum depends on the Sérsic radius and index as well as the seeing.
96% flux aperture: PyDIET uses an aperture large enough to contain approximately 96% of the source flux. It includes most of the source flux but also generally includes more background noise than a strictly optimal aperture.

It is useful when the goal is close to total-flux photometry rather than maximum SNR.
fixed aperture: PyDIET uses a user-specified aperture diameter.

Selecting this option reveals the Aperture diameter field.

The ETC integrates the source model inside the specified aperture and computes the sky and detector noise over the corresponding number of pixels. A small aperture reduces sky noise but misses more source flux. A large aperture captures more source flux but includes more sky background. The best value depends on the seeing, source morphology, and science goal.

Aperture diameter

The Aperture diameter field is shown only when fixed aperture is selected. The value sets the aperture diameter in arcseconds.

Sky brightness

The Sky brightness menu selects the background model.

Available choices are:

dark: selects the dark-time sky model, with the Moon at the nadir. PyDIET uses a predefined sky emission spectrum for dark conditions. This spectrum contributes background photons in each pixel and therefore affects the noise term.

In optical bands, the dark-sky emission model is dominated by the airglow and continuum components. In the near infrared, it features strong OH emission and thermal terms.
grey: selects the intermediate lunar-background model, with a 30% Moon component (66.4° phase angle), a lunar elevation of 45°, and a separation of 45° from the telescope's line of sight.

Compared with the dark model, the sky count rate increases, reducing the SNR for background-limited observations or increasing the exposure time needed to reach a target SNR.
bright: selects the high-background lunar sky model, with a 60% Moon component (101.5° phase angle), a lunar elevation of 45°, and a separation of 45° from the telescope's line of sight. The impact is strongest in blue and optical bands. It is much less dominant in near-infrared bands where OH airglow and thermal background already contribute strongly.
specify: enter the sky brightness manually. When it is selected, two additional fields appear: Sky value and Sky unit.

PyDIET uses your value to set the sky brightness. This is useful for matching a measured background or reproducing known observing conditions.

Sky value

The Sky value field sets the numerical value of the manually specified sky brightness. It is shown only when Sky brightness is set to specify.

Sky unit

The Sky unit menu selects the unit used for the manual sky brightness.

Available choices are:

AB mag.arcsec⁻²: the sky value is interpreted as an AB surface brightness.

PyDIET converts the AB surface brightness into a photon rate per unit angular area, then into electrons per pixel using the pixel scale, throughput, and detector quantum efficiency.
Vega mag.arcsec⁻²: the sky value is interpreted as a Vega-based surface brightness.

PyDIET converts the Vega surface brightness through the selected bandpass. The AB-Vega offset is filter-dependent.
MJy.sr⁻¹: the sky value is interpreted as a surface brightness in megajanskys per steradian.

This is a common infrared surface-brightness unit. PyDIET converts it to a flux density per angular area and then to detected electrons per pixel through the selected filter and throughput model.
flux.arcsec⁻²: the sky value is interpreted as a physical flux per square arcsecond, in units of 10^-15erg.s^-1.cm^-2.arcsec^-2.

PyDIET converts the physical sky flux into a photon/electron rate over the selected bandpass. This option is primarily meant to quantify backgrounds through narrow-band filters, or for matching an external sky model.
e⁻.s⁻¹.px⁻¹: the sky value is interpreted directly as a detected electron rate per pixel.

This option bypasses most of the photometric conversion for the sky background. The detector noise model uses the entered value directly as the background count rate, with no added instrumental thermal component.

Airmass

The Airmass field describes the line-of-sight optical path through the atmosphere. The default value is 1.2.

Airmass affects both atmospheric transmission and sky emission. Larger airmass usually reduces source throughput because the source light crosses more atmosphere. It can also increase the sky emission and the contribution from scattered light.

PyDIET interpolates atmospheric transmission and sky emission between spectra tabulated at discrete airmasses.

Solar activity

The Solar activity menu selects the solar-activity level used in the sky emission model.

Solar activity modulates airglow emission. This changes the sky background and hence the SNR, particularly in the near ultraviolet, optical, and some near-infrared airglow features.

Available choices are:

low: corresponds to 70 solar flux units (sfu) in the supplied sky model.

Low solar activity generally reduces some airglow components, especially in the ultraviolet and optical where upper-atmosphere emission can matter. It therefore produces a darker natural sky background than the average or high solar-activity models.
average: corresponds to 130 sfu in the supplied sky model.

This is the default for general planning when more specific information, such as the observing year, is unavailable. It represents a typical sky-emission state averaged over the whole solar cycle.
high: corresponds to a high solar radio flux model, 200 sfu in the current configuration.

Mirror condition

The Mirror condition menu selects the telescope mirror throughput model.

Available choices are:

pristine: represents a freshly coated or nearly freshly coated mirror. This option gives the highest mirror reflectivity. It increases the source count rate and can also increase the sky count rate, since both source and sky photons are reflected by the telescope.

In most source-limited or read-noise-limited regimes, a pristine mirror significantly improves SNR. In strongly background-limited regimes, the gain is more modest because both signal and sky background increase.
average: represents the average mirror state between recoatings.

This is the default and should be used for ordinary planning.

CFHT mirrors are typically recoated every three years. As zero-point degradation is roughly linear with time, the average mirror condition corresponds to 1.5 years after recoating.
degraded: represents an older or less reflective mirror coating.

This option further reduces telescope throughput.

At CFHT, this corresponds to three years after recoating.

Transparency

The Transparency field is a generic, multiplicative atmospheric transparency factor between 0 and 1.

The default value is 1.0.

Transparency scales source light relative to the nominal atmospheric model by the same factor at all wavelengths (grey absorption), leaving the sky background unchanged. A value of 1.0 represents nominal clear conditions. A lower value represents additional attenuation from clouds, cirrus, aerosols, or other non-photometric conditions, reducing the SNR for a given exposure time.

Submitting a calculation

After selecting the desired parameters, press Submit.

PyDIET sends the form values to the server and displays the calculation in a result panel.

Results

The result panel shows the exposure time and SNR, along with supporting quantities:

Instrument name: the instrument that was selected in the settings panel.
Filter name: the filter selected for that instrument.
Pivot wavelength: a measure of the effective wavelength of the combined instrument+atmospheric response \(T(\lambda)\). It is defined as the wavelength that makes the broadband conversion between \(f_\nu\) and \(f_\lambda\) exact for this bandpass:

\[\lambda_{\rm piv} = \sqrt{\frac{\int T(\lambda)\lambda d\lambda}{\int T(\lambda)\lambda^{-1} d\lambda}}.\]
Rectangular bandwidth: the width of an ideal top-hat filter with the same integrated throughput and peak transmission as the combined instrumental and atmospheric response \(T(\lambda)\):

\[\Delta\lambda_{\rm rect} = \frac{\int T(\lambda)\, d\lambda}{T_{\rm max}}.\]
Signal-to-noise ratio: the ratio between the expected signal from the (stacked) photometric source measurement and its standard deviation.
Exposure time: the exposure time per image needed to reach the requested SNR in the combined measurement, or the supplied exposure time when calculating SNR.
Background saturation time: the expected exposure time required to saturate the combined sky+instrumental background.
Source saturation time: the expected exposure time required to saturate the source peak signal.
Total time (including overheads): the sum of exposure times and instrumental overheads for the whole observation sequence.
Full photometric magnitude zero-point (per second): estimated AB magnitude zero-point of the combined instrument and atmosphere for a one-second exposure.
Background surface brightness (in mag.arcsec^-2): estimated surface brightness (in AB magnitudes per square arcsecond) of the combined sky+instrumental background.

|PyDIET| result panel — Fig. 2 Example result panel.

Caveats

The ETC result is only as accurate as the adopted model. The current model ignores the following effects:

source crowding and contamination by neighboring objects;
imperfect flat-fielding;
systematic background-subtraction errors;
PSF variations over the field of view;
detector persistence and nonlinearity;
fringing or scattered light;
changing sky transparency during the exposure sequence;
cosmic-ray hits and cosmetic defects;
calibration uncertainties;
observer-specific reduction choices.

For critical observing programs, use PyDIET as one input to the planning process and compare with measured performance from similar observations when available.