AUSTRALIAN NATIONAL UNIVERSITY System Design Note 5.21 Created: 12 April 2000 Last modified: 1 August 2000

NIFS GRATING SELECTION

Ian Price

Research School of Astronomy and Astrophysics

Institute of Advanced Studies

Australian National University

Revision History

Revision No.	Author & Date	Approval & Date	Description
Revision 1	Ian Price 20 August 1999		Original document.
Revision 2	Ian Price 01 November 1999		Added theoretical blaze functions.
Revision 3	Peter J. McGregor 21 December 1999		Changed grating selection and discussed grating efficiencies and anamorphic magnification.
Revision 4	Peter J. McGregor 12 April 2000	Jan van Harmelen 12 April 2000	Reformatted for Word 2000.
Revision 5	Peter J. McGregor 12 April 2000	Jan van Harmelen 13 April 2000	Updated after CoDR.
Revision 6	Peter J. McGregor 01 August 2000	Jan van Harmelen 01 August 2000	Added L band gratings and alternative configurations.

Contents

1 Purpose. 2

2 Applicable Documents. 2

3 Introduction. 2

4 Optimal Wavelength Range. 2

5 Optimal Spectral Resolving Power. 5

6 Grating Selection Criteria. 7

7 Grating Selection. 8

7.1 Grating Option A: 26.3 mm Beam Configuration. 8

7.2 Grating Option B: 19.7 mm Beam Configuration. 11

7.3 Which Grating Option?. 12

7.4 L Band Gratings. 13

7.5 Alternative configurations with a Rotary Grating Mechanism.. 13

8 Scattered Light 13

9 Grating Manufacture. 14

10 Field Viewing Mirror. 14

11 Appendix: Grating Identifications. 14

Appendix: List of Figures. 15

1 Purpose

The purpose of this document is to describe the diffraction gratings that will be available in the Gemini Near-infrared Integral-Field Spectrograph (NIFS) and to define the criteria that have been used in making the grating selection.

2 Applicable Documents

Document ID	Source	Title
SDN0004.01	RSAA	NIFS Performance Model
SDN0005.06	RSAA	NIFS Diffraction Analysis

3 Introduction

The Gemini Near-infrared Integral-Field Spectrograph (NIFS) is a low-cost, fast-tracked instrument. As such, the choice of reflection gratings is restricted to commercially available catalog gratings and only one fixed-format spectrograph camera will be available. The selection of grating parameters and camera focal length are a trade between spectral coverage, spectral resolving power, signal-to-noise ratio, and OH airglow emission-line rejection efficiency. The science drivers for NIFS require spectral resolving powers R ³ 5000 in the J and H bands to significantly separate OH airglow lines, and velocity resolutions of ~ 100 km s^-1 (corresponding to spectral resolving powers R ~ 3000) to measure stellar velocity dispersions in nearby galactic nuclei. NIFS is also required to provide coverage of as much as possible of the 0.95-2.50 mm wavelength range having atmospheric transmission above ~ 50% from Mauna Kea. Suitable grating sets for use in NIFS are identified below, and their characteristics are discussed.

4 Optimal Wavelength Range

NIFS will record spectra in the full wavelength range over which the transmission of the Earth’s atmosphere exceeds ~ 50%. NIFSSIM (NIFS Performance Model, SDN0004.01) atmospheric transmission spectra for Mauna Kea in the J, H, and K bands are shown in Figure 1, Figure 2, and Figure 3. The wavelength ranges corresponding to > 50% transmission are l < 1.35 mm, 1.44 < l < 1.81 mm, and 1.95 < l < 2.50 mm for the J, H, and K bands, respectively. The background emission spectra corresponding to these wavelength ranges are shown in Figure 4, Figure 5, and Figure 6.

Figure 1: J band atmospheric transmission with the 50% transmission range shaded.

Figure 2: H band atmospheric transmission with the 50% transmission range shaded.

Figure 3: K band atmospheric transmission with the 50% transmission range shaded.

Figure 4: J band background emission spectrum with the 50% transmission range shaded.

Figure 5: H band background emission spectrum with the 50% transmission range shaded.

Figure 6: K band background emission spectrum with the 50% transmission range shaded.

5 Optimal Spectral Resolving Power

NIFS will record data at moderate spectral resolution and use software suppression to reject OH airglow emission during data reduction. The choice of optimal spectral resolving power depends on the required level of OH rejection and on the science requirements of the instrument. NIFSSIM (NIFS Performance Model, SDN0004.01) has been used to calculate the fraction of each of the J, H, and K photometric bands that is blocked by OH airglow emission in spectra recorded at different resolving powers (Figure 7, Figure 8, and Figure 9); as the spectral resolving power increases the fraction of wavelength space occupied by OH emission decreases. The K band OH blocking fraction was calculated over only the short wavelength part of the band containing OH emission. What constitutes an acceptable level of OH blocking depends on the science goals. Measurements of specific spectral features at low redshift may require a low blocking fraction, whereas high redshift galaxies can often be selected in particular redshift ranges and so higher blocking fractions can be tolerated. We subjectively adopt a maximum allowable blocking fraction of 20%. This requires spectral resolving powers greater than 3200, 3800, and 2750 in the J, H, and K bands, respectively.

The spectral resolving power should be chosen to maximize the signal-to-noise ratio achieved, consistent with the required OH blocking fraction and the resolution requirements dictated by the science goals. Figure 7, Figure 8, and Figure 9 also show NIFSSIM predictions for the average signal-to-noise ratios achieved in 1800 s in a 0.1²´0.1² aperture on stars with J = 20 mag, H = 20 mag, and K = 19 mag, respectively, for observations recorded at different spectral resolving powers and then smoothed to a common resolving power of R = 1000. The signal-to-noise ratios were calculated from the mean and standard deviation of data values in spectra of a featureless input star, after correction for atmospheric absorption. In each figure, the solid line shows the signal-to-noise ratios achieved when regions containing OH emission are excluded from the calculation, while the dot-dash lines show the signal-to-noise ratios achieved with no OH rejection. Higher signal-to-noise ratios are achieved in OH-free regions of the J and H bands in spectra recorded at progressively lower resolving powers. This is due to the lower relative contributions of dark current and read noise in low resolution spectra. However, only small fractions of the bands are OH-free at these low resolving powers. The dot-dash lines are applicable in these case where OH rejection is not possible. It is apparent from Figure 7 and Figure 8 that the optimal spectral resolving powers in both the J and H bands are the minimum values that are consistent with the required OH blocking fraction and the science requirements. Observations in the K band are background-limited. Figure 9 demonstrates that the signal-to-noise ratio achieved at R = 1000 is largely independent of the resolving power of the observation (the increasing signal-to-noise ratios at higher resolving powers occur because the high background, long-wavelength end of the K band is progressively excluded from the high resolution simulations). The spectral resolving power that should be used in the K band is again defined by the required OH blocking fraction and science requirements, but the actual value has little impact on the signal-to-noise ratio achieved at R = 1000.

Figure 7: J band fractional blocking due to OH airglow emission versus spectral resolving power (left) and signal-to-noise ratio in 1800 s on a J = 20 mag star versus spectral resolving power (right) with OH lines masked (solid line) and with no OH line masking (dot-dash line).

Figure 8: H band fractional blocking due to OH airglow emission versus spectral resolving power (left) and signal-to-noise ratio in 1800 s on a H = 20 mag star versus spectral resolving power (right) with OH lines masked (solid line) and with no OH line masking (dot-dash line).

Figure 9: K band fractional blocking due to OH airglow emission versus spectral resolving power (left) and signal-to-noise ratio in 1800 s on a K = 19 mag star versus spectral resolving power (right) with OH lines masked (solid line) and with no OH line masking (dot-dash line).

6 Grating Selection Criteria

NIFS is designed with a minimum of cryogenic mechanisms in order to simplify and speed its construction, assembly, and commissioning phases. It was decided early-on to include only one grating wheel carrying fixed-angle gratings, rather than to develop a complex cryogenic mechanism for selecting different gratings and setting and accurately maintaining the required grating angle. Consequently, each NIFS grating is optimized for its particular pass band. All gratings are selected to operate in first order for maximum efficiency. Only gratings with groove spacings significantly larger than the maximum operating wavelength were considered initially; groove densities of 600, 400, and 300 l mm^-1 are the finest considered for the J, H, and K bands, respectively. Gratings are chosen to operate at low grating angle, q, to maintain high grating efficiency and minimize polarization effects. With the above constraint on the groove density and the mechanical constraint that the Ebert angle, f, must be ~ 30°, grating angles of ~ 20° are required to center each of the H and K bands on the detector. The angles used for all gratings should be similar to ensure that the monochromatic slitlet image width is always matched to two detector pixels.

For grating angles of up to 20°, the spectral resolving power is determined by the angular slitlet width as

where d_col is the diameter of the collimated beam, d_tel is the diameter of the telescope aperture, and dg_x is the angular slit width. For grating angles of more than 20°, the spectral resolving power is determined by the pixel size as

where f_cam is the camera focal length, and dh_x is the pixel size. The resolving power using a grating angle q = 20° is therefore ~ 5300. The collimator beam diameter has been chosen so that the H band (1.49-1.80 mm) fills the detector with a 400 l mm^-1 grating. A 300 l mm^-1 grating operating at an angle of 20° in the K band then delivers the wavelength range 2.00–2.41 mm to the detector, which covers about 75% of the K band available from Mauna Kea. Two gratings are therefore required to cover the full accessible K band. Two gratings are also required to cover the available J band. The grating selection is then dictated by the availability of suitable blaze functions.

Applying the pupil aperture over-sizing factor specified in the diffraction analysis (NIFS Diffraction Analysis, SDN0005.06) gives an active grating length of 51 mm. Gratings with smaller ruled masters were not considered. The gratings will be mounted on the face of a 300 mm diameter wheel. The size of this wheel is limited by the duplicate NIRI cryostat dimensions. Eight gratings of this length can be accommodated on the grating wheel. Fewer is preferred to improve stability. One of these positions will be allocated to a mirror for direct viewing of the undispersed image (§10).

7 Grating Selection

7.1 Grating Option A: 26.3 mm Beam Configuration

The 26.3 mm beam configuration is the baseline optical design. A suitable grating set delivering R ~ 5300 is listed in Table 1. Littrow relative efficiency curves for these gratings have been obtained from the Richardson Grating Laboratory; these are all > 80% in their operating bands (Figure 10). However, the K grating does not cover the full atmospheric window.

Table 1: R ~ 5300 Gratings for the 26.3 mm Beam Configuration

Grating	central wavelength (mm)	Grooves (l/mm)	Grating Blaze (degrees)	Grating Angle (degrees)	Resolving Power	Velocity Resolution (km/s)	Spectral Coverage (mm)
J1	1.05	600	17.5	19.0	4990	60.1	0.94-1.15
J2	1.25	600	22.0	22.8	6040	49.6	1.15-1.35
H	1.65	400	18.6	19.9	5280	56.8	1.49-1.80
K	2.20	300	17.5	20.0	5300	56.6	2.00-2.41

Figure 10: Littrow relative efficiency curves for gratings in Table 1 in s-plane (solid line) and p-plane (dashed line) polarized light. The wavelength range used for each grating is shaded. The reflectivity of aluminum is plotted as a heavy solid line.

Full coverage of the K band can be achieved in two exposures using two K gratings mounted at different angles. The parameters for these gratings are listed in Table 2. Littrow relative efficiency curves for these gratings are shown in Figure 11. No efficiency curve has yet been obtained for the Kl grating so it has been estimated by shifting the Ks grating curve in Figure 11.

Table 2: R ~ 5300 K Band Gratings for the 26.3 mm Beam Configuration

Grating	central wavelength (mm)	Grooves (l/mm)	Grating Blaze (degrees)	Grating Angle (degrees)	Resolving Power	Velocity Resolution (km/s)	Spectral Coverage (mm)
Ks	2.15	300	17.5	19.5	5145	58.3	1.95-2.36
Kl	2.29	300	22.0	20.8	5510	54.4	2.09-2.50

Figure 11: Littrow relative efficiency curves for the Ks (left) and Kl (right) gratings listed in Table 2. Other features are as for Figure 10.

Broader spectral coverage in the K band with a single exposure can be achieved at the expense of spectral resolving power by substituting the coarser Kw grating in Table 3 for the K grating listed in Table 1. The Kw grating offers wavelength coverage over the full K band available from Mauna Kea. The poorer velocity resolution delivered by this grating is appropriate for stellar velocity dispersion measurements in nearby galactic nuclei, but is not sufficiently high for Galactic interstellar medium studies such as resolving velocity structure in jets from young stellar objects. Furthermore, the Kw grating has poor efficiency over the required operating band (Figure 12) with a peak in-band efficiency (polarized at 45º to the grooves) of ~ 78% at 1.9 mm and a minimum of ~ 32% at 2.5 mm. The low efficiency of the Kw grating means that this lower resolution grating would produce a lower signal-to-noise ratio per pixel than the higher resolution K grating. The Kw¢ grating 15.0° groove angle is expected to have a better blaze profile. No efficiency curve has yet been obtained for this grating so it has been estimated by shifting the Kw grating curve in Figure 12.

Table 3: Kw Gratings for the 26.3 mm Beam Configuration

Grating	central wavelength (mm)	Grooves (l/mm)	Grating Blaze (degrees)	Grating Angle (degrees)	Resolving Power	Velocity Resolution (km/s)	Spectral Coverage (mm)
Kw	2.17	200	10.0	13.0	3240	92.7	1.84-2.51
Kw¢	2.17	200	15.0	13.0	3240	92.7	1.84-2.51

Figure 12: Littrow relative efficiency curves for the Kw (left) and Kw¢ (right) gratings listed in Table 3. The curve for the Kw grating is for light polarized at 45º to the grooves. Other features are as for Figure 10.

Broader wavelength coverage with approximately half the resolving power of the gratings in Table 1 and Table 2 can also be achieved using the J and HK gratings listed in Table 4. The whole J atmospheric window is recorded in one exposure of a HAWAII-2 2048´2048 array with the J grating, and all of the K band along with half of the H band is recorded with the HK grating. The HK grating would also permit the measurement of Pa at low redshift on nights with suitable transparency, but the coverage does not extend sufficiently shortward to reach the important [Fe II] 1.644 mm emission-line. The relative efficiency of the J grating has not been measured by the Richardson Grating Laboratory. The relative efficiency of the HK grating is poor (Figure 13) with large s- and p-plane polarization differences. Consequently, this grating will not realize the potential signal-to-noise ratio improvement from halving the spectral resolving power. Furthermore, spectra obtained with the low resolving power J and HK gratings will be severely contaminated by OH airglow emission-lines (§5).

Table 4: Low Resolution Gratings for the 26.3 mm Beam Configuration

Grating	central wavelength (mm)	Grooves (l/mm)	Grating Blaze (degrees)	Grating Angle (degrees)	Resolving Power	Velocity Resolution (km/s)	Spectral Coverage (mm)
J	1.15	300	10.4	10.3	2510	119.4	0.92-1.38
HK	2.08	150	8.6	9.3	2250	133.2	1.62-2.54

Figure 13: Littrow relative efficiency curves for the HK grating listed in Table 3. Other features are as for Figure 10.

7.2 Grating Option B: 19.7 mm Beam Configuration

An alternative way of broadening the K band wavelength coverage is to scale the whole spectrograph to a smaller size. The full K band accessible from Mauna Kea is made available with the K grating listed in Table 1 if this scale factor is 0.748. The collimated beam diameter is then 19.7 mm, the collimator focal length is 315 mm, and the camera focal length is 215 mm. The four gratings from Table 1 perform in the way listed in Table 5 in this configuration. The wavelength coverage of each grating is increased by ~ 30%, causing the H grating to extend well into regions of poor atmospheric transmission, and broadening the coverage of the J1 and J2 gratings so that they can overlap significantly in the region of poor atmospheric transmission around 1.12 mm. Indeed, the coverage of the J2 grating is sufficient that it may be unnecessary to include the J1 grating. The resolving power achieved with each grating is also reduced by the scaling factor and is ~ 3970 for grating angles of ~ 20°. Values of R ³ 4000 are still sufficient to adequately separate OH airglow line emission (§5). The lower resolving power also helps overcome dark current noise in the J and H bands. Relative efficiency curves for these gratings are repeated in Figure 14 with their now wider operating bands.

Table 5: R ~ 4000 Gratings for the 19.7 mm Beam Configuration

Grating	central wavelength (mm)	Grooves (l/mm)	Grating Blaze (degrees)	Grating Angle (degrees)	Resolving Power	Velocity Resolution (km/s)	Spectral Coverage (mm)
J1	1.07	600	17.5	19.4	3830	78.4	0.93-1.21
J2	1.22	600	22.0	22.3	4420	67.8	1.09-1.35
H	1.62	400	18.6	19.6	3870	77.5	1.41-1.83
K	2.22	300	17.5	20.2	4020	74.7	1.95-2.50

Figure 14: Littrow relative efficiency curves for the gratings listed in Table 5. Other features are as for Figure 10.

The combined H and K bands can now be covered at R ~ 1600 with the low efficiency HK grating (Table 6). Similarly, the entire J band can be covered at R ~ 1800 with the J’ grating listed in Table 6, with large overlap into the optical. The relative efficiency curves for these gratings are shown in Figure 15. The main advantage of these gratings is their large wavelength coverage.

Table 6: Optional Gratings for the 19.7 mm Beam Configuration

Grating	central wavelength (mm)	Grooves (l/mm)	Grating Blaze (degrees)	Grating Angle (degrees)	Resolving Power	Velocity Resolution (km/s)	Spectral Coverage (mm)
J¢	1.10	300	8.6	9.8	1780	168	0.79-1.40
HK	1.95	150	8.6	8.7	1570	191	1.34-2.57
K1	2.12	497	34.0	33.0	6620	45.3	1.98-2.25
K2	2.32	497	34.0	36.6	7410	40.5	2.19-2.44
Jh	1.25	830	30.0	32.5	6500	46.2	1.15-1.35
Hh	1.62	600	28.7	30.2	6015	49.9	1.48-1.76

Figure 15: Littrow relative efficiency curves for the gratings listed in Table 6. The curve for the J¢ grating is for light polarized at 45° to the grooves. Other features are as for Figure 10.

The overall lower resolving powers of the moderate resolution gratings (Table 5) are primarily a concern in the K band where higher resolution is required to measure Brg 2.166 mm and H₂ 1-0 S(1) 2.122 mm emission-line profiles and stellar velocity dispersions in cool systems using the 2.3 mm CO first-overtone bands. However, there is also a need for higher resolving power in the J2 and H bands for measuring rotation curves of small z ~ 1 galaxies. Somewhat higher resolving powers can be achieved in the K band using the K1 and K2 gratings listed in Table 6. The same grating master delivers R ~ 7000 over the K atmospheric window in two grating settings with good efficiency (Figure 15). The Jh grating listed in Table 6 delivers a similarly high resolving power in the wavelength region of Ha in z = 0.75-1.05 galaxies. The Hh grating listed in Table 6 delivers only slightly higher resolving power than the H grating, so is probably not worthy of inclusion. Efficiency curves for the Jh and Hh gratings are yet to be obtained.

An advantage of this configuration is that the spectrograph would be significantly smaller and therefore easier to accommodate in the duplicate NIRI cryostat.

7.3 Which Grating Option?

NIFS can accommodate seven gratings and a direct viewing mirror, although a smaller number is to be preferred. Option B can be rejected based on the generally lower two-pixel resolving powers delivered, and the concern that these will be reduced further when realistic optical aberrations are included. The five Option A shown in Table 7 are selected as the baseline grating suite for NIFS. The Kw¢ grating is also worthy of consideration for measurements of stellar velocity dispersion in galaxies.

Table 7: Baseline Grating Suite with 26.3 mm Beam

Grating	central wavelength (mm)	Grooves (l/mm)	Grating Blaze (degrees)	Grating Angle (degrees)	Resolving Power	Velocity Resolution (km/s)	Spectral Coverage (mm)
J1	1.05	600	17.5	19.0	4990	60.1	0.94-1.15
J2	1.25	600	22.0	22.8	6040	49.6	1.15-1.35
H	1.65	400	18.6	19.9	5280	56.8	1.49-1.80
Ks	2.15	300	17.5	19.5	5145	58.3	1.95-2.36
Kl	2.29	300	22.0	20.8	5510	54.4	2.09-2.50

7.4 L Band Gratings

NIFS may use a detector with a 5 mm wavelength cut-off. There are no plans to use NIFS in the 5 mm band. However, it may be possible to simply extend operation to 4.2 mm by including L band gratings. A suitable choice of L band grating configurations for the 26.3 mm beam is shown in Table 8.

Table 8: L Band Grating Configurations

Grating	central wavelength (mm)	Grooves (l/mm)	Grating Blaze (degrees)	Grating Angle (degrees)	Resolving Power	Velocity Resolution (km/s)	Spectral Coverage (mm)
Ls	3.33	150	13.0	15.0	3795	79.0	2.90-3.75
Ll	3.73	150	13.0	16.8	4290	69.9	3.30-4.15

7.5 Alternative configurations with a Rotary Grating Mechanism

The use of a rotary mechanism to interchange gratings opens the possibility of using gratings at angles other than their baseline design angles. In particular, it becomes possible within the constraints of the grating blaze function to use each grating at lower grating angle to achieve lower resolving powers than those defined in the baseline configuration in shorter wavelength bands. Alternative configuration options for the baseline 26.3 mm beam gratings are listed in. .Table 9

Table 9: Alternative Grating Configurations

Grating	central wavelength (mm)	Grooves (l/mm)	Grating Blaze (degrees)	Grating Angle (degrees)	Resolving Power	Velocity Resolution (km/s)	Spectral Coverage (mm)
J’	1.19	400	18.6	14.3	3580	83.8	1.06-1.35
H’	1.65	300	17.5	14.9	3750	80.0	1.44-1.86

8 Scattered Light

Scattering at the grating may prove to contribute significantly to near-angle scattering of OH airglow line emission into the adjacent continuum. This would degrade the efficiency with which airglow emission-lines can be rejected. The Richardson Grating Laboratory has been asked to quantify this effect. No data are currently available. However, replicated gratings may actually have lower scattered light levels due to the smoothing of surface defects by the epoxy and inversion of the grooves. In any event, short of ruling new master gratings, there is nothing that can be done to reduce this scatter.

9 Grating Manufacture

Richardson Grating Laboratories can produce replica gratings on client supplied substrates. The recommended substrate for cryogenic applications is aluminum. The surface roughness tolerance is 25 mm RMS. The perpendicularity tolerance between adjacent sides is 0.1°. The grating side of the substrate must have a 45° bevel edge, with 1.5 mm face width.

10 Field Viewing Mirror

The case for a field-viewing plane mirror in the grating wheel is two-fold; it would allow the undispersed “staircase” slit image to be recorded to aid in acquiring faint objects, and it could also be used to check the alignment of the IFU. Of course, a field-viewing mirror is unnecessary if sufficiently accurate object and guide star coordinates are known in advance. However, many situations can be envisaged where it will be advantageous to image the sky directly through NIFS to confirm critical positioning or alignments. The data cube generated from NIFS spectral data can be collapsed in the spectral direction to produce an image of the sky. However, this image inherits the dark current and read noise from all 2048 spectral pixels recorded at each spatial location. It is more efficient to obtain an image by replacing the grating with a plane mirror and directly recording the undispersed image of the “staircase” slit. Wavelength stability should not be affected by rotating the grating wheel between science observations since the grating angles will be fixed and the wavelength calibration should not be sensitive to small positioning errors of the grating perpendicular to the optical axis.

Imaging the “staircase” slit directly will allow the alignment of the IFU to be inspected as well as providing a spatial calibration of the IFU pattern on the detector. This is not a strong motivation for including a field-viewing mirror since similar information can be obtained from an arc lamp spectral image without using a field-viewing mirror.

11 Appendix: Grating Identifications

The Richardson Grating laboratory catalog numbers and master dimensions of all the gratings discussed are listed in Table 10 for future reference.

Table 10: Grating Catalog Numbers and Master Dimensions.

Grating	Grooves (l/mm)	Grating Blaze (degrees)	CATALOG Number	RULED AREA (mm´mm)
J1	600	17.5	35-53-*-520	154´206
J2	600	22.0	35-53-*-560	154´206
H	400	18.6	35-53-*-650	102´102
K, Ks	300	17.5	35-53-*-770	154´206
Kl	300	22.0	35-53-*-736	102´102
Kw	200	10.0	35-53-*-630	84´84
Kw’	200	15.0	35-53-*-636	154´206
J	300	10.4	35-53-*-640	84´84
HK	150	8.6	35-53-*-760	154´206
J’	300	8.6	35-53-*-510	102´128
K1,K2	497	34.0	35-53-*-231	102´102
Jh	830	30.0	35-53-*-525	154´206
Hh	600	28.7	35-53-*-550	154´206
Ll,Ls	150	13.0	35-53-*-690	154´206

Appendix: List of Figures

Figure 1	jatmos.gif
Figure 2	hatmos.gif
Figure 3	katmos.gif
Figure 4	jbkg.gif
Figure 5	hbkg.gif
Figure 6	kbkg.gif
Figure 7	jblocking.gif
Figure 8	hblocking.gif
Figure 9	kblocking.gif
Figure 10	j1j2hka.gif
Figure 11	kskla.gif
Figure 12	kwkwa.gif
Figure 13	kwhka.gif
Figure 14	j1j2hkb.gif
Figure 15	j_hk_k1_k2.gif