fig3 shows the varying focus of the beam according to the solidified region , preferably , when using a pulsated laser ; fig4 is a perspective and schematical representation of a positioning device for an inventive sensor ; the representation of the inventive apparatus in fig1 shows a layer 1 of a material which can be solidified using electromagnetic radiation , for example a polymerizeable liquid or paste or a sinterable powder material , as well as a solidifying device 2 arranged above the layer for solidifying the material of the layer 1 at the places corresponding to the object to be produced . the solidifying device 2 comprises a radiation source 3 formed as a laser and directing a focused light beam 4 to a deflection device 5 operable to deflect the light beam 4 to the desired places of the layer 1 . to this end the deflection device is connected to a control unit 6 for corresponding control of the deflection device 5 . between the light source 3 and the deflection device 5 there are subsequentially arranged in the light beam 4 a modulator 7 and a variable focusing device 8 which are also connected to the control unit 6 for control in the manner described further below . the modulator may for example be formed as an acousto - optical , electro - optical or mechanical modulator and serves as &# 34 ; switch &# 34 ; for pulsing or interrupting , respectively , the beam 4 . the variable focusing device 8 serves to change the focus of the beam 4 . as shown in more detail in fig2 it comprises to this end a concave dispersing lens 9 and a convex focusing lens 10 following each other in direction of the beam 4 . the focusing lens 10 may for example be positioned in direction of the beam 4 between the position shown in dotted lines and the position shown in full lines in fig2 and varies the focus and therefore the diameter of the beam at the working or reference plane 11 , which may for example be the surface of the layer 1 , according to its position . the displacement of the focusing lens 10 is made by a ( not shown ) displacement device using a step motor or servo motor connected to the control unit 6 . the arrangement of the two lenses 9 , 10 may be replaced by any other suitable multiple lens arrangement with a focus variation by displacing two lenses relative to each other . instead of using the variable focusing device 8 the deflection device 5 may comprise deflection mirrors having an adjustable variable radius of curvature . in this case the focus of the beam 4 can be varied by changing the radius of curvature of the deflection mirrors . between the deflection device 5 and the layer 1 there is further arranged a sensor 12 which can be moved to each place above the layer 1 in a plane parallel thereto , and preferably immediately above the layer 1 using the positioning device 13 shown in more detail in fig4 . the positioning device 13 is formed as an x , y positioning device whereby the sensor 12 is displaceable in a first x direction along the upper side of a wiper 14 extending across the layer 1 in x direction and being movable across the layer 1 in y direction for adjusting a desired layer thickness of the material . in another embodiment the sensor may also be positioned independently of the wiper . the sensor output is connected to the control unit 6 . a first embodiment of the sensor 12 is shown in fig5 . the sensor 12 according to fig5 is formed as a quadrant sensor having a light sensitive member formed as a photodiode 15 , 16 , 17 , 18 disposed in each quadrant . the photodiode 18 of one quadrant is covered by an opaque cover , for example a small metal plate 19 , having a diaphragm aperture 20 in the center thereof . according to a second embodiment shown in fig6 the sensor 12 is formed as a single sensor having a single field with a light sensitive member formed as a photodiode 21 disposed therein , whereby the photodiode is again covered by an opague cover , for example a small metal plate , with the exception of a central diaphragm aperture . the diameter of the diaphragm aperture 20 , 23 is between about 20 μm and 50 μm , preferably 35 μm . in operation the laser beam 4 is first measured with regard to its position , power and diameter . the position detection is made using the sensor 12 shown in fig5 by positioning the sensor 12 at a predetermined defined x , y location and using the control unit 6 to control the deflection device 5 so that the deflected beam 4 passes over the sensor 12 and travels from the field of the photodiode 15 to that of the photodiode 16 . the output signals of both photodiodes are compared ; if both signals are equal the position of the beam 4 exactly corresponds to the transition between both fields of the photodiodes and thus to the central position of the sensor 12 . a corresponding measurement is made for the transition from the photodiode 15 to the photodiode 17 . by comparing the positional data obtained with the corresponding desired position of the deflection means 5 it is determined whether the adjustment of the beam 4 is correct or a disadjustment exists . in the latter case the control in the control unit 6 is corrected or a readjustment of the appartus is made . the positional measurement is carried out by moving the sensor 12 to various positions above the layer surface 1 corresponding to arbitrary places within the area of irradiation using the positioning device 13 so that the positioning accuracy at the solidifying device 2 can be exactly determined . however , it is also possible to measure only at selected points , for example at two points , to detect a global drift for example caused by a temperature variation . this drift can then be compensated again by corresponding correction of the control unit 6 or of the control software stored therein , respectively . the power of the beam 4 can be determined by direct processing of the output signals of the photodiodes 15 , 16 and 17 with the amplitude thereof corresponding to the power . also pyroelements may be used of this purpose . by comparison with nominal values again a defect of the solidifying device 2 can be detected , for example , dusting of the optical system , aging or even failure of optical or electronic components . for the purpose of measuring the diameter of focus of the beam 4 the deflection device 5 and / or the positioning device 13 is controlled so that the deflected beam 4 passes over the diaphragm aperture 20 of the sensor according to fig5 or over the diaphragm aperture 23 of the sensor according to fig6 along two coordinate directions . thus , the intensity profile of the beam 4 is scanned and the focus or diameter of the beam 4 is calculated using the obtained intensity data of the profile . this measurement can be made in the entire irradiation area or at selected points only , for example in connection with the power measurement . again , a deviation caused for example by aging of the laser or a disadjustment of the optical system can be detected by comparison with corresponding nominal values . in this case , a certain correction can be made by varying the focus by means of control of the variable focusing device 8 . when using the sensor 12 shown in fig6 the position and power of the beam 4 is determined with the aid of calculations , i . e . the position as calculated by determining the intensity maximum and the power is calculated by integration of the profile . such calculations are known and are therefore not explained in detail . after adjusting and measuring the beam 4 a material layer 1 is applied and solidified by concerted irradiation of the layer 1 at the places corresponding to the object using the deflected beam 4 . fig3 shows a region 24 which includes , as an example , the places to be solidified of the layer . for solidification this region is divided into an outer envelope region 25 and an inner core region 26 , whereby the envelope region 25 , preferably completely , encloses the core region 26 . for solidification the control unit 6 controls the variable focusing device 8 , the deflection device 5 and the laser 3 in such a manner that the layer is irradiated with a smaller beam diameter or focus indicated by the small circles in the envelope region 25 and with a larger beam diameter or focus , as indicated by the larger circles , in the core region 26 . this results in a finer and more accurate solidification of the material in the envelope region 25 forming the surface or contour of the object . according to a preferred development the deflection device 5 is controlled so that the speed of the deflected beam 4 passing over the layer 1 ( i . e . the scanning speed ) is higher in the core region than in the envelope region 5 , whereby the production time is considerably reduced . this measure is particularly useful in connection with a high power of the laser 3 , because the power density even with a larger beam diameter or focus is then still sufficient for solidification even at higher scanning speeds . when using a power - adjustable light source for this case the power for solidifying the envelope region 25 can be reduced to adjust the energy or power density to a value suitable for solidification . the above - described method is particularly preferred in connection with a pulsed laser used as radiation source 3 . usually , the pulse rate of such lasers is too low to obtain high scanning speeds with a small focus . rather , only single spaced places are solidified in this case . on the other hand , the average power of this laser decreases above a certain pulse rate . further , the pulse duration , of for example frequency multiplied solid - state lasers is very short ( about 30 ns ). the energy or power density input into the material can no longer be adjusted by varying the scanning speed but only by controlling the attenuation , the repetition rate of the laser and / or the beam diameter . according to the invention it has been found that an operation with best efficiency is obtained by adjusting the beam diameter . an optimum repetition rate in connection with a maximum scanning speed then results from the predetermined value of the beam diameter . at a lower scanning speed the energy input and accordingly the overlap of the places can be increased . according to the invention a short production time in combination with a high structural resolution is obtained for pulsed lasers by solidifying using a smaller focus in the envelope region 25 and a larger focus in the core region 26 and correspondingly adjusting the scanning speed and the repetition rate so that in both regions the areas 27 solidified with each pulse overlap and thereby form a continuous line . this is shown in fig3 : since the admissible scanning speed is proportional to the diameter of the beam or focus 27 which is shown as circle in fig3 the scanning speed in the core region 26 can be increased with respect to that of the envelope region 25 by the factor defining the increase of the diameter in the core region . moreover , correspondingly less scanning lines are required in the core region 26 . thus , the production time decreases with the square of the relative diameter increase . in both regions 25 , 26 the repetition rate and the beam focus and therefore the average power of the laser results from the corresponding scanning speed which gives a small average power in the envelope region 25 and a larger average power in the core region 26 . for adjusting the focus the control unit 6 varies the position of the focussing lens 10 relative to the dispersing lens 9 by axial displacement dependent upon whether the deflection device 5 directs the beam 4 to the core region 26 or to the envelope region 25 . the corresponding control data are stored in the control unit 6 . preferably , the envelope region 25 is first solidified using a small focus and thereafter the focus is increased and the core region 26 is solidified with the focus being once adjusted to this increased value . again , the focus adjustment of the beam can be measured and corrected using the sensor 12 in the above - explained manner . the further layers of the object are applied and solidified in the same manner . the beam can be measured as described above before producing an object but also between the solidification of individual layers or at larger intervals , for example day by day . detected deviations from admissible values can also be displayed on a display device . preferably , diode pulsed neodym yag laser or diode pulse neodym ylf laser having a power of about 300 mw are used as solid - state lasers .