referring now to fig6 there is shown a somewhat schematic view of an alignment apparatus according to an embodiment of the present invention . fig7 is a flow chart showing the operation of the apparatus of fig6 . the same reference numerals as in fig1 are assigned to the corresponding elements in fig6 . as shown in fig6 a wafer 1 is provided with a left side alignment mark ( hereinafter simply called &# 34 ; mark &# 34 ;) lw and a right side mark rw . above the wafer 1 , there is a mask 2 provided with a left side mark lm and right side mark rm , corresponding to the wafer marks lw and rw , respectively . the wafer 1 and the mask 2 are in close proximity with each other , or are positioned in optically conjugate relation with respect to a projection optical system not shown . the references ow and om are the centers of the area 1a of the wafer 1 to be exposed and the pattern area 2a of the mask 2 ; and cm and cw are respective one of the corners of the pattern area 2a and the exposure area 1a . the wafer 1 is fixedly supported by , for example , a vacuum chuck on a stage mechanism which is movable in x - direction and y - direction by a wafer stage driving mechanism 7 . deviation measuring means 3l and 3r are disposed above the mask 2 to determine the deviations between the marks lm and rm of the mask 2 and the marks lw and rw of the wafer 1 , respectively . the outputs of the deviation measuring means 3l and 3r are transmitted to a first processing means or circuit 4 and then to second processing means or circuit 5 . a data input means 6 is effective to transmit the desired position information from the pattern area 2a and the exposure area 1a to the first processing means 4 . further , the data input means 6 is adapted to receive the size and the configuration of a tolerance area for the positional deviation between the mask 2 and the wafer 1 and to receive the size ( 2a × 2b ) of the pattern area 2a and the exposure area 1a . the data in this respect are transmitted to the second processing means 5 . the operation of the apparatus will now be described in conjunction with fig7 - 9 . as shown in the flow chart of fig7 at the beginning , the positional deviation , ( δxl , δyl ) and ( δxr , δyr ), is detected between the marks lm and rm of the mask 2 and the corresponding marks lw and rw of the wafer 1 , respectively by the deviation measuring means 3l and 3r ( fig6 ). this is the step 20 in the fig7 . at the second step , that is , step 21 , the first processing circuit 4 calculates the positional deviation ( δx o , δy o ), between the center om of the pattern area 2a and the center ow of the exposure area 1a of the wafer 1 and calculates a rotational deviation δθ o between the pattern area 2a and the exposure area 1a . as shown in fig8 the central deviations δx o and δy o , and the rotational deviation are calculated by the following equations : where the coordinate positions of the marks lm and rm on the mask coordinate om - xm - ym are (- xm , ym ) and ( xm , ym ), respectively . the data of the mark positions ( xm , ym ) are given by the data input means 6 . at the third step , i . e ., a step 22 , the second processing means 5 calculates the maximum deviations δxmax and δymax , which are the maximum deviations in the pattern area 2a . the size of the pattern area 2a is given to the second processing means 5 through the data input means 6 as a rectangular area having the edge of length a in the x - direction and the edge of length b in the y - direction , that is , the pattern area 2a is defined by - a ≦ x ≦ a , - b ≦ y ≦ b in the mask coordinate . also , the data of the tolerance for the deviation are given for the purpose of the fourth step , that is , step 23 . at a given point p ( xc , yc ) on the pattern area 2a , the deviation from the point on the exposure area 1a , to which the point p exactly corresponds , is : since , | xc |≦ a and | yc |≦ b , the maximum deviations in the pattern area are : at the fourth step , that is , step 23 , the second processing means 5 discriminates whether the maximum deviations δxmax and δymax are within the tolerance on the basis of the following inequations : when those inequations are satisfied , the proper alignment operation is deemed to have been accomplished . if not , the wafer 1 is moved by the wafer stage driving mechanism 7 to correct the deviations , and then the process goes back to the first step , that is , the step 20 . according to the above described process of alignment operation , the alignment is rejected at the fourth step ( step 23 ) if there is at least one point in the pattern area where the deviation is beyond the tolerance , that is , | δx |& gt ; t or | δy |& gt ; t . therefore , the alignment is complete only when the deviation is not more than the tolerance t at any point in the pattern area . the position data ( xm , ym ) which is necessary in the calculation at the step 21 , the pattern area data ( a , b ) necessary for the calculation at the step 22 and the tolerance data ( t ) necessary for the calculation at the step 23 , are inputted by the data input means 6 prior to the start of the alignment routine . therefore , the system can meet the change of the alignment mark positions , the change of the pattern area size and / or the change of the required tolerance . however , it is a possible alternative that the data input means 6 is omitted , and the data are fixed in the processing means 4 and 5 , when the sizes of the mask and wafer and the positions of the marks are fixed . in the foregoing embodiment , the wafer 1 is moved to correct the deviation , it is possible to move the mask 2 or to move both of the mask 2 and the wafer 1 . in the foregoing embodiment of fig6 and 7 , the description has been made with respect to the tolerance area having a rectangular configuration , that is , | δx |≦ t and | δy |≦ t at any point in the pattern area . however , it is not always necessary that the tolerance area be rectangular . for example , when a diamond - shape tolerance area is desired as shown in fig4 the following discriminating inequalities is used at the fourth step , that is , step 23 of fig7 in place of the inequalities ( 8 ) and ( 9 ): as another example , when a circular area of tolerance is desired at any points on the pattern area , the circle having radius t , the following discriminating inequality is used : thus , the shape and / or the size of the tolerance area can selectively be set by the data input means 6 . in the foregoing embodiment , the deviation data have been described as being obtained at two positions , ( δxl , δyl ) and ( δxr , δyr ). however , this is not limiting , and any type of measuring method are usable if both the translational deviation and the rotational deviation can be obtained between two objects . further , in the foregoing embodiment , the description has been made as to the method or device whereby any point in the pattern area is brought into the same tolerance , but this is not limiting in the present invention . rather , it is possible to change the tolerance depending on the position in the pattern area , or to change the shape of the tolerance area depending on the position in the pattern area . as has been described , according to the present invention , the alignment in the desired precision can be accomplished in the minimum time required . further , if means is provided for setting both or one of the size and the shape of the tolerance area , the alignment operation can be accomplished in the minimum time depending on the size and / or the shape of the tolerance area . while the invention has been described with reference to the structures disclosed herein , it is not confined to the details set forth and this application is intended to cover such modifications or changes as may come within the purposes of the improvements or the scope of the following claims .