The efficiency of a grating is a parameter which gives the percentage of
energy concentrated in a given order and in a given wavelength. More this
efficiency approach 100% better is the grating for the wavelength considered.
This page gives the efficiency of various transmission gratings, not
very expensive, and usable in the convergent beam of the telescope for
low spectral resolution observation. I measured this efficiency by using
an Helium-Neon laser and an Audine camera as detector. So, the efficiency
is given for the wavelength of 632.8 nm.
The table below shows the result for 4 gratings easy to find: the Cokin
grating, the Jeulin grating, the Edmund Scientific grating and the Rainbow
Optics grating. Order higher than 2 are ignored in this study because of
their weak contribution in general. But because of this approximation one
can to estimate that all the values of efficiency are overestimated from
2 to 3 % approximately.
|
Reference
|
Conditioning
|
Efficiency
|
Cokin N# 40
240 lines/mm
Cost: 300 FF - $45 |
|
Order +2 : 2,2 %
Order +1 : 5,3 %
Order 0 : 85,0 %
Order -1 : 5,3 %
Order -2 : 2,2 % |
Jeulin
100 lines/mm
Cost: 123 FF - $20 |
|
Order +2 : 2,3 %
Order +1 : 43,0 %
Order 0 : 47,3 %
Order -1 : 5,6 %
Order -2 : 1,8% |
Edmund Scientific
70 lines/mm
Cost: 1700 F - $260 |
|
Order +2 : 10,7 %
Order +1 : 56,5 %
Order 0 : 30,4 %
Order -1 : 1,1 %
Order +1 : 1,2 % |
Rainbow
Optics
200 lines/mm
Cost: 2400 F - $370
1593 "E" Street, Hayward, CA 94541
Tel : (510) 581-8266 |
|
Order +2 : 0,7 %
Order +1 : 67,6 %
Order 0 : 22,5 %
Order -1 : 6,6 %
Order -2 : 2,6 % |
When placing the grating wery close to the CCD, image
quality feels some. Figure 1 shows the spots diagrams for several wavelength
when there engraved surface of the Rainbow grating is placed 8 mm in front
of the surface of the CCD (dispersion of 55 A/pixel).
Figure 1. Spot-diagrams calculated
in a configuration where the the Rainbow Optics grating is located 8 mm
in front of the CCD. Telescope caracteristics: focal length of 760 millimeters,
F/D=4, and central obstruction of 0,4. From left to right, zero order image,
300 nm image, 500 nm image, and 700 nm image. The green circle simulates
the size of a star (FWHM) covering two pixels when one uses a KAF-0400
CCD (9-microns pixels size). This equivalent to a seeing of about 4 arc-seconds.
Graduations are in millimeters.
The analysis of the images of figure 1 shows a chromatic coma which
one can reduce by introducing a wedge prism of small angle into the beam,
just in front of grating. This prism can be integrated easily in the barrel
of the Rainbow grating if it has a diameter of 25 mm, as shows figures
2 and 3.
Figure 2. Top, the Rainbow Optics
transmission grating. Bottom, a 3°52' wedge prism (origin Edmund Scientific).
Figure 3. The 25 millimeters diameter
prism into the Rainbow barrel (grism configuration).Note that the orientation
of the prism relative to the grating grooves is critical.
Nominaly, the deviation of the prism compensate the deviation of the grating
at the central wavelength
With a prism of angle 3.87° (H43651 reference in the Edmund Scientific
catalog, material: BK7, thickness: 3.0 mm) one obtains the spots images
of figure 4.
Figure 4. Same convention that
for figure 1. The use of a prism in front of the Rainbow grating reduce
the chromatic coma appreciably. The field curvature is now the prevalent
aberration. The CCD was focused for the wavelength of 0,5 µm where
the image is quasi stigmatic. The residual coma can be cancelled by choosing
a prism of more large angle (about 5 or 6°), but under these conditions
the astigmatism increases quickly and the benefit of the correction of
the chromatic coma cancels. The compromise carried out here is almost ideal.
The aberrations are now of the same order of the seeing. The theoritical
spectral resolution is of 9 nm.
The blue extended spectral
sensitivity of the KAF-0401E is very usefull for spectrography. I tested
this CCD in an Audine camera by observing SAO83560, a star of the spectral
type A0V and of magnitude 6.9 (RA=14h52m07.37s, DEC=+20°17' 27.6").
The dispersive element, in the convergent beam of the 190 mm telescope,
is the Jeulin grating of 100 lines/mm. The grating is located 52.8 mm in
front of the CCD. The final image is the result of the combining of two
90 seconds frames.
Figure 5. Spectral
profile of star SAO83560. The spectrum is not calibrated, but some lines
were identified. The mark on the left is towards 3200 A. The green rectangle
highlights the additional part of the spectrum which it is possible to
observe with the KAF-0401E compared to the KAF-0400. Dispersion is 16.9
A/mm.
Figure 6. Enlarging of the
blue part of the spectrum of SAO83560. The line H-epsilon would be problematic
to observe with a standard KAF-0400. The H&K lines of CaII are
accessibles. These lines, which have a great astrophysical importance,
are very easily accessible with the KAF-0401E. The green arrow indicates
the position of the Balmer discontinuity at 3647 A.