Sol'Ex configurations

Characteristics of Sol'Ex configurations used for measuring filters and etalons

Note the M42 focusing ring on the collimator tube (both collimating and ilmaging lenses are focused depending on the wavelength used).

Theoritical spectral resolution is calculated using Simspec (developped by Ken Harrison).

The collimated and imaging lenses are assummed to be diffraction limited : FWHM = lambda × f-number

Configuration	Dispersion near Ca II	Dispersion near Ha	Theoritical spectral resolution near Ca II	Theoritical spectral resolution near Ha
80 mm f.l. collimator + 2400 l/m grating + 125 f.l. mm imaging lens + ASI 290	0.093 A/px	0.075 A/px		0.22 A
125 mm f.l. collimator + 1200 l/m grating + 125 f.l. mm imaging lens + ASI 290	0.193 A/px	0.192 A/px		0.70 A
125 mm f.l. collimator + 2400 l/m grating + 125 f.l. mm imaging lens + ASI 290	0.0933 A/px	0.0755 A/px (measured)		0.20 A
125 mm f.l. collimator + 2400 l/m grating + 125 f.l. mm imaging lens + 2.22× Barlow + ASI 290		0.0336 A/px (measured)
200 mm f.l. collimator + 2400 l/m grating + 200 f.l. mm imaging lens + 10 microns slit + ASI 290	0.0582 A/px (measured)	0.0471 A/px (measured)	0.18 A	0.15 A
200 mm collimator + 2400 l/mm grating + 200 mm imaging lens + 7 microns slit + ASI 290			0.15 A	0.14 A
10 micron slit + 200 mm collimator + 3600 l/mm grating + 200 mm imaging lens + 2.9 micron pixel sensor	0.0347 A/px		0.087 A

Measured spectral resolution using fine lines of the solar spectrum

Configuration	FWHM for Ca K	FWHM for Ha
10 micron slit + 125 mm collimator + 2400 l/mm grating + 125 mm imaging lens + 2.9 micron pixel sensor	about 0.20 A	between 0.17 to 0.18 A
125 mm collimator + 2400 l/m grating + 125 mm imaging lens + 2.22× Barlow + 2.9 micron pixel sensor		between 0.15 to 0.16 A
10 micron slit + 200 mm collimator + 2400 l/mm grating + 200 mm imaging lens + 2.9 micron pixel sensor	about 0.16 A	between 0.15 to 0.16 A
7 micron slit + 200 mm collimator + 2400 l/mm grating + 200 mm imaging lens + 2.9 micron pixel sensor	about 0.14 A	between 0.15 to 0.16 A
10 micron slit + 200 mm collimator + 3600 l/mm grating + 200 mm imaging lens + 2.9 micron pixel sensor	better than 0.10 A

Measurement of SHG spectral resolution using thin lines in the solar spectrum

Some interesting lines (Ca II, G-band, Mg triplet, Na, Ha)

Measurement of the linewidth of a hydrogen lamp

Interference fringes in the cover slit of sensor

Measurement of SHG spectral resolution using thin lines of the solar spectrum

Some definitions first:

The spectral resolution of a spectroscope can be defined in several ways.
It is usually defined as the ability to distinguish between two wavelengths separated by a small amount Δλ and expressed in terms of the dimensionless quantity: R = λ / Δλ

Another way to look at it is through the "bandpass" of the spectroscope, in other words, the FWHM of a monochromatic line observed with the spectroscope:

Using this definition, we can compare the bandpass of a SHG with the bandpass of an etalon (all expressed in Angström).

We can note an analogy with the resolution of optical telescopes:
- the angular resolution (Resolving Power) of a telescope can be defined as the ability to distinguish the two components of a double star. A common relationship is : RP = 120/D, where RP is in arsec and D is in mm,
- another way to define the resolution of a telescope is the FWHM of the image of a star observed at its focus. The theoretical relationship is: FWHM = lambda/D
- the "response" function of the telescope is called the Point Spread Function (PSF). The FWHM is the width measured at the half maximum of the PSF profile.
In a same way, for a spectroscope, the "response" function is the "Line Spread Function (LSF). This is the image of a monochromatic line produced by the spectroscope.

NB : difference between spectral resolution (A) and dispersion (A/pixel).
Spectral resolution should not be confused with dispersion.
Going to the analogy with the angular resolution of a telescope:
- spectral resolution (A) is the analog of "angular resolution (arsec)",
- while "dispersion (A/pixel)" is the analog of sampling (arsec/pixel).

Methodology:

Ideally, in order to measure the spectral resolution of a spectroscope, we would measure the FWHM of a monochromatic line.

However, when we look at the solar spectrum, even the thinnest lines have a sizable FWHM. In addition, the thinner the line the lower the contrast, which makes it them more difficult to measure accurately.
So, have to take into account the "true" FWHM of the measured lines in order to calculate the spectral resolution (FWHM_spectro) of the spectroscope.

The procedure is as follows:
- measurement of the true FWHM (FWHM_true) of a very thin line of the solar spectrum using the very high resolution solar spectrum of BASS2000 (dispersion = 0.002 A/px),
- measurement of the FWHM (FWHM_measured) of the same line with the spectroscope. Compared to the true FWHM of the line, the measured FWHM is broaded by the "response function" of the spectrograph.
- if we call FWHM_spectro the bandwidth of the spectroscope, we have the relationship:
FWHM_measured² = FWHM_true² + FWHM_spectro²

Reference "thin" lines near Ha:

The three following "thin" lines are used for the measurements:
- Fe I at 6546.25 A with true FWHM = 0.127 A,
- ATM at 6548.62 with true FWHM = 0.0537A,
- ATM at 6552.6A with true FWHM = 0.0589 A.

The true FWHM of these lines was measured by fitting a Voigt function to their profiles extracted from BASS2000 very high resolution solar spectrum.

Measuring the "true" FWHM of Fe I at 6546.25 A: Measuring the "true" FWHM of ATM 6448.62 A using BASS2000:

Reference "thin" lines near Ca K:

The following "thin" lines are used for the measurements:
-Ti 3924.5 A (FWHM = 0.077 A)
- Fe I 3925.2 A (FWHM = 0.081 A).
Both are labelled hereafter with cross marks:

The true FWHM of these lines was measured by fitting a Voigt functon to their profile taken from BASS2000 high resolution solar spectrum:

1) 10 micron slit, 125 mm f.l. collimating lens, 2400 l/mm grating, 125 mm f.l. imaging lens, ASI290

Spectral resolution near Ha:

The following figure illustrates the measured profile of the ATM6548.61 A line (green dots) and the fit with a Voigt function (yellow curve).

The measured FWHM is 2.38 pixels × 0.0755 (A/pixel) = 0.180 A.
Given that the true FWHM of the line is 0.0537 A, the spectral resolution of the spectroscope is equal to:     square root ( FWHM_measured² - FWHM_true²) = 0.173 A.
Using the average over the three spectral lines described above, the spectral resolution of the spectroscope near Ha was found to be in the range of 0.17 to 0.18 A.

Spectral resolution near Ca K:
The collimating lens was refocussed on Ca K.
The FWHM of the Ti line at 3924.5A was measured (30 April 2022):             FWHM_mesured = 2.33 pixels = 0.217 A.
Given that the true FWHM of the line is 0.077 A, the spectral resolution of the spectroscope is equal to:     square root ( FWHM_measured² - FWHM_true²) = 0.20 A.

NB : the Fe I line at 3925.2 A was not measurable.


2) 10 micron slit, 200 mm f.l. collimating lens, 2400 l/mm grating, 200 mm f.l. imaging lens, ASI290

Spectral resolution near Ha :
The FWHM of the ATM H₂O line at 6548.62 A was measured at 0.167 A (curve fitting with Voigt function).

Taking into account the true bandwidth of the line, we get a spectral resolution in the range of 0.15 to 0.16 A.

Spectral resolution between Ca K and H :
The measured FWHM is 0.17 A for the finest lines (measurement is made difficult because of the densitry of spectral lines near Ca II). Resulting spectral resolution is FHWM_spectro = 0.16 A.

3) 10 micron slit, 200 mm f.l. collimating lens, 3200 l/mm grating, 200 mm f.l. imaging lens, IMX585

Spectral resolution near Ca K:
Using the Fe I line at 3937.33 A, we measured a spectral resolution better than 0.10 A.
(measured 19 May 2025)

4) 7 micron slit, 200 mm f.l. collimating lens, 2400 l/mm grating, 200 mm f.l. imaging lens, ASI290

Spectral resolution near Ha :
Measured FWHM 3.42 x 0.0471 = 0.161 A (curve fitting by Voigt function, 20 points sampling, using the ATM H₂O line at 6548.62 A).
Resulting spectral resolution : 0.0152 A

Spectral resolution near Ca K :
FHWM_measured for Ti line at 3924.5 A = 2.53 x 0.0582 = 0.147 A (curve fitting by Voigt function, 10 points sampling).
Given that the true FWHM of this line si 0.077 A, we can estimate the spectral resolution at: FWHM_spectro = 0.14 A

5) 10 micron slit, 125 mm f.l. collimating lens, 2400 l/mm grating, 125 mm f.l. imaging lens + 2.22× Barlow lens, ASI290

Spectral resolution near Ha :
Using the three "thin" lines described above, we have spectral resolution = 0.15 to 0.16 A

Field coverage of the Thorlabs 200 mm f.l. lens:

About 6 mm in diameter in Ca II and Ha, which is comparable to the length of Solex gen 2 slit (6 mm).

Ca II K and H lines

Sol'Ex V2 configuration: 10 micron slit, 200 mm f.l. collimating lens, 2400 l/mm grating, 200 mm f.l. imaging lens, ASI290:

Solar limb taken with the Takahashi TOA150 and Sol'Ex V2. Visible beyond the photospheric limb are Ca K3(absorption), Ca K2r and v (emisison), Ca H3 (absorption), H2r and v (emission), and H epsilon lines:

Sol'Ex V1 configuration: 10 micron slit, 125 mm f.l. collimating lens, 2400 l/mm grating, 125 mm f.l. imaging lens, ASI290:
Top image : reference very high resolution solar spectrum with lines labelled. Bottom : spectrum obtained with Sol'Ex.

Sol'Ex V0 configuration: 10 micron slit, 80 mm f.l. collimating lens, 2400 l/mm grating, 125 mm f.l. imaging lens, ASI290:

Sol'Ex V2: configuration: 10 micron slit, 200 mm f.l. collimating lens, 2400 l/mm grating, 200 mm f.l. imaging lens, ASI290:

Sol'Ex V0: configuration: 10 micron slit, 80 mm f.l. collimating lens, 2400 l/mm grating, 125 mm f.l. imaging lens, ASI290:

Sol'Ex configuration: 10 micron slit, 80 mm f.l. collimating lens, 2400 l/mm grating, 125 mm f.l. imaging lens, ASI290: