a Fig. 6
(negatwes) I” Fig. 2 using
of the grid dlffractlon plane
Conclusions A method for producing binary. linear and grid gratings with arbitrary opening ratios and variable periods has been presented which uses the properties of Fresnel images of Ronchi type binary linear gratings. The method. as compared with one presented earlier (see Ref. 2) gives the possibility of producing diffraction gratings using only a single exposure and allows the observation and measurement of the grating parameters before photographic registration. Moreover. an opening ratio value between 0 and 1 can be obtained. The disadvantages of the method are the necessity of using two or four master gratings and the necessity of producing one or three of these gratings (being the self-images of the first) in the case of using spherical wave illumination. The number of gratings may be reduced when plane wave illumination is used. Applying the system shown in Fig. 4 it is possible to produce the linear grating and the grid gratings with one or two master gratings only. When the lateral shift of the grating is introduced the arrangement shown in Fig 4 is fully equivalent to the one presented in this paper. It is also possible to propose a method where producing additional master gratings is not necessary. The required period value may be obtained by producing a grating with an arbitrary opening ratio and a period equal to one half of the master grating period. see the set-up shown in Fig I. and then making an additional copy of this grating under spherical wave illumination’. This method also has other limitations caused by the diffraction of light on the periodic objects and the inaccuracy of the optical elements. The most important weakness is due to the presence of phase distortions introduced by the photographic emulsion and the substrate of the master gratings. The influence of this phenomenon can be reduced by inserting the master gratings into the immersion cell.
of a -
Another disadvantage results from the so called ‘walkoff’effcct. especially when gratings of high density are produced. For reducing this effect the gratings should be put close enough to each other (the best solution is to put the second grating in the first self-image of the first grating) but this can be inconvenient if one uses gratings of high density (for example. the distance of the first self-image for a grating of 40 lines mm-’ is I.9 mm). In addition. if the grating planes are not exactly parallel to the plane of the photographic plate. then errors occur in the image being recorded. All these facts inlluencc the quality of the final product and mukc production of gratings of greater than 40 lines mm 3 very difficult.
Acknowledgement I wish to thank I1r K_ Patorski for his valuable remarks and suggestions concerning the final shape of this paper and for continuous assistance during its preparation.
References Burch, J.M. ‘Proprcss in Optics‘ North-Hollnncl Amsterdam 75 Patorski, K. ‘Production of binary amplitude gratings with arhitrery opening ratio and variable period’ Opr Lrr.wr ~dlno/ I2 (I’)XO)267-270 Patorski, K., Sznaykowski, P. ‘Producing and tcating hinary amplitude gratings using a seltlimaging and douhleexposure technique‘ Opr Ltrsw Twhnol 15 (19X3) 3lh-320 Szwaykowski, P., Patorskii K. ‘Properties of the Fresncl field of the tlouhle diffraction systsem’ ./ Opr 16 (19X5)95103 Winthrop, J.T., Worthington, C.R ‘Theory ol’ Fresncl image 1. Plant periodic objects in monochromatic light‘ J Opr Sot, Am 55 ( 1965) 37?-3x I Cohen-Sabban, Y. Yoyeux D. ‘Aberration-free nonparaxial beIf-imaging J Opt SockAm 73 (1983) 707-719
OPTICS AND LASER TECHNOLOGY.
CO2 laser welding
of copper slabs
M. DELL’ERBA For the first time it has been possible thick with a 2 kW cw CO2 laser. The are indicated. KEYWORDS:
to laser weld copper sheets main questions arising from
the layer thickness X = 10.6 pm.
Laser welding of copper has recently been carried out on sheets up to 3 mm thick. The source used was a 2 kW BOC cw CO, laser. whose beam was focused by a 10 cm %nSe lens. Two assistance gases. helium and oxygen. were used simultaneously. The copper surface was as supplied and uncoated.
of the oxide. respectively.
In Fig, 2, a micrographic section of laser welded 2 mm thick copper sheet_ obtained at a speed of 5 mm SK’ (which is not the critical one) is shown.
Penetration welding of copper can essentially be described in the same way as that obtained on other metals. The main difference lies in the time required for the formation of the keyhole at the beginning of the process. because of the thermophysical properties of copper. In fact. when the laser radiation impinges on the target. its high reflectivity at 10.6 pm permits only the absorption of a small part of the incident energy. At the same time, the energy absorbed is quickly removed from the interaction point due to the high thermal conductivity. Then. the temperature rises slowly and the formation of the keyhole is consequently delayed.
However. when the temperature becomes higher than 700 “C. an oxide layer (of both CuO and Cu,O. see Ref. 1) begins to grow on the sample surface near the interaction point As reported by I. Ursu et al2 when taking into account the interference phenomena in metal-oxide layer systems, the absorption coefficient of the copper. A,, changes according to A,
Equation (1) clearly shows the dependence of the absorption coefficient on the square of the layer thickness which, in turn. is a function of the sample temperature. As a consequence, after the process is primed the absorption of the target is greatly enhanced because of the oxides spreading over the surface with a variable thickness, depending on the isotherm distribution. The laser welding of copper can thus be performed up to a critical speed, which seems to be mainly a function of the metal thermal conductivity value, and which is less dependent on other experimental conditions.
In Fig 1 the experimental set-up is schematically shown with the laser radiation perpendicularly impinging on the target surface at the focal point Helium as the shielding gas. flows coaxially with the laser beam while the oxygen is fed through a nozzle directly onto the interaction point The < angle between the sample plane and the oxygen nozzle axis seems to be a function of the experimental conditions. including the sample thickness. Penetration
up to 3 mm the process
A,,( I + 47r((nZ -
where A,, is the initial value of the absorption coefficient n and-u are the refractive index and The
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0030-3992/85/050261-02/$03.00 OPTICS AND
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