<p>The basic grating equation is
<span class="math-container">$$\sin \theta_d = \frac{n \lambda}{d} - \sin \theta_i\ , $$</span>
where <span class="math-container">$\lambda$</span> is the wavelength of light, <span class="math-container">$d$</span> is the groove spacing on the grating, <span class="math-container">$\theta_i$</span> is the angle to the grating normal of the incident light (this is fixed and independent of wavelength) and <span class="math-container">$\theta_d$</span> is the angle to the normal of the diffracted light. <span class="math-container">$n$</span> is the &quot;order&quot; of the diffration and is an integer - <span class="math-container">$n=1, 2...$</span></p>
<p>Your spectrum is formed by diffracting light of different wavelengths at different <span class="math-container">$\theta_d$</span> and recording the signal on a CCD. If you are using a diffraction grating say at red wavelengths with <span class="math-container">$n=1$</span>, then it is possible to get blue light diffracted at the same angle if <span class="math-container">$n=2$</span>. This would make your spectrum uninterpretable, since your detected spectrum would be an inseparable mixture of blue and red light (astronomical CCDs are monochrome of course). Normally, you would use a broad &quot;order sorting&quot; filter so that you do not get unintended pollution of your light from a different diffraction order.</p>
<p>For example, if you intended to collect a spectrum at 700-900 nm in order 1, then you don't want it polluted by light at 350-450 nm in order 2. By inserting the GG455 G0329 you make sure that light with <span class="math-container">$\lambda &lt; 450$</span> nm cannot reach the detector.</p>
<p>Spectrographs with really broad wavelength coverage would usually have some arrangement to ensure that light of different wavelengths cannot fall on the same pixels on the detector - having multiple arms and detectors, with a dichroic to split the light (e.g., <a href="https://www.ing.iac.es/astronomy/instruments/isis/" rel="nofollow noreferrer">ISIS on the WHT</a>) or a cross-disperser to separate the orders perpendicular to the dispersion (mostly high resolution, echelle spectrographs), or even both (like <a href="https://www.eso.org/sci/facilities/paranal/instruments/xshooter/overview.html" rel="nofollow noreferrer">Xshooter at the VLT</a>). GMOS does not have these capabilities and a blocking filter must be used when doing spectroscopy at <span class="math-container">$\lambda &gt; 660$</span> nm unless for some reason you know your objects are invisible at wavelengths of <span class="math-container">$\lambda/2$</span>.</p>
<p>EDIT: You didn't say whether you were using GMOS in long-slit or multi-object slit-mask mode. If the latter, then an additional reason for using a filter is to shorten the recorded spectrum so there is less chance of an overlap with the spectrum of another object in the same slit mask, especially if the field might be observed at various rotation angles.</p>

CC BY-SA 4.0
2023-12-28T16:39:37.327Z
2023-12-28T17:03:29.977Z
2023-12-28T17:03:29.977Z
ProfRob
<p>I am considering writing a proposal for using the GMOS with the R150 grating. I want to measure the redshift of multiple systems from the strong lensing effect of some clusters, so the redshift range is wide (1&lt;z&lt;5). Therefore, it is better if the wavelength coverage is broad. However, when I use any filter as shown in the figure below, the wavelength range becomes narrower. Additionally, there is a loss in Signal-to-Noise (S/N) ratio if I use any filter.</p>
<p>For example, when I use the 'GG455 G0329' filter, there is a loss of the blue wavelength range and S/N compared to when I use no filter.</p>
<p>For me, it seems the best option is not to use any filter. Am I right?</p>
<p><a href="https://i.sstatic.net/p9Tpy.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/p9Tpy.jpg" alt="Filter system for GMOS-S" /></a></p>
<p>P.S. I also add the grating efficiency of R150 below.</p>
<p><a href="https://i.sstatic.net/5KuqU.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/5KuqU.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2023-12-28T11:02:43.240Z
Are there any filters that have a wide enough bandwidth so that the radiation is not attenuated at the required frequencies? Is it possible to design a filter with a given bandwidth?
ayr
<spectroscopy><filter>
Why is the filter needed for low resolution GMOS spectroscopy?
BAO
# Why is the filter needed for low resolution GMOS spectroscopy?

(Asked by: username_0 on 2023-12-28)

I am considering writing a proposal for using the GMOS with the R150 grating. I want to measure the redshift of multiple systems from the strong lensing effect of some clusters, so the redshift range is wide (1<z<5). Therefore, it is better if the wavelength coverage is broad. However, when I use any filter as shown in the figure below, the wavelength range becomes narrower. Additionally, there is a loss in Signal-to-Noise (S/N) ratio if I use any filter.

For example, when I use the 'GG455 G0329' filter, there is a loss of the blue wavelength range and S/N compared to when I use no filter.

For me, it seems the best option is not to use any filter. Am I right?

[![Filter system for GMOS-S](https://i.sstatic.net/p9Tpy.jpg)](https://i.sstatic.net/p9Tpy.jpg)

P.S. I also add the grating efficiency of R150 below.

[![enter image description here](https://i.sstatic.net/5KuqU.png)](https://i.sstatic.net/5KuqU.png)

**Tags:** spectroscopy, filter

> **Comments:**
> **username_1**: Are there any filters that have a wide enough bandwidth so that the radiation is not attenuated at the required frequencies? Is it possible to design a filter with a given bandwidth?  

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## 1 answers

### Answer by username_2 on 2023-12-28. Score: 2 | Accepted answer

The basic grating equation is
$$\sin \theta\_d = \frac{n \lambda}{d} - \sin \theta\_i\ , $$
where $\lambda$ is the wavelength of light, $d$ is the groove spacing on the grating, $\theta\_i$ is the angle to the grating normal of the incident light (this is fixed and independent of wavelength) and $\theta\_d$ is the angle to the normal of the diffracted light. $n$ is the "order" of the diffration and is an integer - $n=1, 2...$

Your spectrum is formed by diffracting light of different wavelengths at different $\theta\_d$ and recording the signal on a CCD. If you are using a diffraction grating say at red wavelengths with $n=1$, then it is possible to get blue light diffracted at the same angle if $n=2$. This would make your spectrum uninterpretable, since your detected spectrum would be an inseparable mixture of blue and red light (astronomical CCDs are monochrome of course). Normally, you would use a broad "order sorting" filter so that you do not get unintended pollution of your light from a different diffraction order.

For example, if you intended to collect a spectrum at 700-900 nm in order 1, then you don't want it polluted by light at 350-450 nm in order 2. By inserting the GG455 G0329 you make sure that light with $\lambda < 450$ nm cannot reach the detector.

Spectrographs with really broad wavelength coverage would usually have some arrangement to ensure that light of different wavelengths cannot fall on the same pixels on the detector - having multiple arms and detectors, with a dichroic to split the light (e.g., [ISIS on the WHT](https://www.ing.iac.es/astronomy/instruments/isis/)) or a cross-disperser to separate the orders perpendicular to the dispersion (mostly high resolution, echelle spectrographs), or even both (like [Xshooter at the VLT](https://www.eso.org/sci/facilities/paranal/instruments/xshooter/overview.html)). GMOS does not have these capabilities and a blocking filter must be used when doing spectroscopy at $\lambda > 660$ nm unless for some reason you know your objects are invisible at wavelengths of $\lambda/2$.

EDIT: You didn't say whether you were using GMOS in long-slit or multi-object slit-mask mode. If the latter, then an additional reason for using a filter is to shorten the recorded spectrum so there is less chance of an overlap with the spectrum of another object in the same slit mask, especially if the field might be observed at various rotation angles.


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