Spectrometer design, calibration and characteristics

I have applied a home-built 2D imaging spectrometer in our FTSSI setup which is an extension of the conventional Czerny-–Turner imaging spectrometer. Figure 2.12 shows notations and the basis of a conventional Czerny-–Turner spectrometer which is in fact based on a 4f configuration. In this configuration, the entrance slit S, the plane grating G and the 2D detector D are located in the focal planes of the spherical mirrors. The first spherical mirror C collects and collimates the divergent wavefront from the entrance input slit. The diffraction grating disperses angularly the spectral components of the collimated beam. The second spherical mirror F focuses the

spec-tral components on the 2D detector placed at its focal plane. In order to measure

Figure 2.12: Configuration of Czerny-Turner spectrometer:entrance slit S, slit to col-limating mirror length LSC, spherical collimating mirror C with angle of incidence in tangential plane θ_C and radius R_C, collimating mirror to grating distance L_CG, grating G with angles of incidence α and diffractionβ, grating to focusing mirror distanceL_GF, spherical focusing mirror F with angle of incidence in tangential plane θF and radiusRF, focusing mirror to detector distance L_{F D}, and detector D angled θ_Dto beam.

the characteristics of the ultrashort pulses with large spectral bandwidth, imaging spectrometers ought to have a high quality image over a broad spectrum. However, since the spherical mirrors have a different focal length for tangential and saggital planes in the off-axis reflection configuration, the produced image of the entrance slit along tangential plane occurs before the saggital plane (zeroth order astigmatism).

There also exists first order astigmatism which is due to the wavelength dependence of the diffraction angle of the grating β(λ). In more detail, β(λ) causes the incident angle on the focusing mirror F to be also wavelength dependent. Furthermore, the incident point of the optical ray on the focusing mirror will be also wavelength depen-dent which results in wavelength dependepen-dent tangential and saggital imaging planes.

In order to correct the zeroth and first order astigmatism and hence obtain stigmatic images two conditions should be fulfilled. First, for a specific wavelength, the dis-tances of the tangential and saggital images from the focusing mirror should be the same ST(λ0) = SS(λ0) (correction of the zeroth order astigmatism). Secondly, both tangential and saggital image distances should change at the same rate as the distance between the focusing mirror and the detector changes ^∂S_∂λ^T = ^∂S_∂λ^S = ^∂L_∂λ^DF (correction of the first order astigmatism). The zeroth order astigmatism can be corrected by reducing the distance between the input entrance slit and the collimating mirrorLSC. Under such conditions, the grating is under a divergent illumination and its diffraction in the tangential plane introduces an astigmatism that compensates the astigmatism that is introduced by the spherical mirrors. The first order astigmatisms can be corrected by different approaches such as implementation of non spherical (toroidal)

Parameter Value Central wavelength 270 nm

RC 300 nm

R_F 300 nm

θC 5^◦

θF 8^◦

α -4^◦

Γ 600 mm⁻¹

β 24.2^◦

Table 2.2: Basic parameters of the 2D imaging spectrometer.

mirrors [144] or aplanar (cylindrical) grating [145]. Austin et al. [146] showed a sim-pler technique that does not require the replacement of the optical elements. It was only based on modification of optical elements angles and distances with respect to each other. In more detail, the angle of the detector in the tangential plane θD, and the distance from the grating to the focusing mirror of the spectrometer LGF, would compensate the astigmatism for a broad spectral bandwidth. The design of our home-made spectrometer which is done in collaboration with Oxford university is based on divergent illumination and the modifications detailed in [146].

Design

Designing of a 2D imaging spectrometer requires all parameters (e.g. inter-component distances, incident angles and the properties of each optical components) to be known.

In our case, the given parameters are mirror radii, incident angles on grating and mirrors [see Tab. 2.2]. The slit image distance along tangential ST and saggital SS

planes from the focusing mirror are calculated from the imaging equations of each individual optical components. Setting equal ST and SS, zeroth order astigmatism correction condition, yields the distance between the slit and the collimating mirror LSC. The detector distance from the focusing mirror LDF is then computed from setting it equal to the imaging distances. The condition for first order astigmatism

correction is obtained by setting equal the wavelength dependent variation of both the saggital and the tangential slit image and the detector distances from the focusing mirror ^∂S_∂λ^T = ^∂S_∂λ^S = ^∂L_∂λ^DF. It yields the detector angle θD and the distance between grating and the focusing mirrorLGF. Figure2.13shows the layout of our astigmatism free 2D-imaging spectrometer that is built in Oxford considering the parameters of Tab. 2.2. Two planar mirrors are additionally implemented between the collimating mirror and the grating and also between the focusing mirror and the detector to provide enough room for the mounts.

C S

F

M M

G 2D

Figure 2.13: Layout of home-built 2D imaging spectrometer. entrance slit S, collimating mirror C, planar mirror M, grating G, focusing mirror F, 2D detector 2D.

Calibration

In order to use the spectrometer, we should know the dispersion relation on the de-tector (ω = αx) or in other words, find the relationship between each pixel on the detector and the corresponding spectral component of the input pulse. We make several narrow bandwidth holes on different spectral regions of the pulse using the calibrated AOPDF pulse shaper and record the diffracted beam with our imaging spectrometer. By computing the pixel indexes corresponding to the spectral ampli-tude holes we work out the variable α. Once α is calculated, we can perform the pixel to wavelength mapping. However, an important fact that should be mentioned

is that our spectrometer is only corrected for astigmatism and there still exists a dis-tortion aberration. In more detail, each recorded spectral component on the detector is a curved line instead of being a straight line. This effect is more visible using a mercury—argon calibration lamp as an input beam. In Fig. 2.14(a) we can see the curvature of the spectral line. In the presence of the distortion, since each column on the detectorx_n does not correspond to a specific spectral componentω_n, the pixel-to-wavelength mapping should be reconsidered. This is done by measuring the curvature of the spectral line and redoing the mapping process by taking it into account.

x / pix

y / pix

300 310 320 330 340 350

300

Figure 2.14: Specific spectral intensity of a mercury-argon calibration lamp. (a) White line is the intensity average of each position along the spectrometer slity and shows the curvature of the line for a specific wavelength. (b) Intensity distribution of the mercury-argon lamp is recorded by CCD camera using a 25 µm diameter pinhole in the entrance of the spectrometer. It reveals the spatial and spectral resolution of the spectrometer.

Resolution

The spatio-spectral resolution of the spectrometer is measured by replacing the en-trance slit with a 25 µm diameter pinhole and illuminating the spectrometer with a mercury–argon calibration lamp. Figure 2.14(b) shows the imaged spot on the 2D-detector. The detector is a CCD camera (EHD Imaging UK-1158UV) with a pixel size of 6.45 µm. The spatial resolution is 40µm which is obtained by measuring the size of spot at FWHM along the y axis. The spectral resolution is 0.08 nm which is measured by ^∆λ_∆x ×δx where, ∆λ is the wavelength separation of two spectral lines of the calibration lamp, ∆x is their corresponding pixel separation and δx is the width of specific wavelength along the x axis.