Supporting an optical element

A method for supporting an optical element unit comprising an optical element in an optical imaging device, the method comprising:

• using a detection device comprising a plurality of N detection units in a plurality of M degrees of freedom to determine in each case a detection value which is representative of a relative position or orientation of an element reference of the optical element in relation to a primary reference of the detection device in the respective degree of freedom,
• wherein at least one of the following holds:
• each detection unit outputs a detection signal which is representative of a distance and/or a displacement of the detection unit in relation to a secondary reference assigned to the optical element and the respective detection unit, and the optical element unit and the detection device define a detection transformation matrix which is representative of the transformation of the N detection signals into the M detection values;
• and
• an actuating device comprising a plurality of S actuating units in a plurality of R degrees of freedom sets in each case a situation value which is representative of a relative position or orientation of an element reference of the optical element in relation to a primary reference of the actuating device in the respective degree of freedom, and each actuating unit generates an actuating state at an interface of the actuating unit with respect to the optical element unit;
• wherein the optical element unit and the actuating device define an actuating transformation matrix which is representative of the transformation of the S actuating states into the R situation values, and the condition number of a transformation matrix is defined by the ratio of the largest singular value of the transformation matrix to the smallest singular value of the transformation matrix;
• and
• wherein at least one of the following holds:
• the condition number of the detection transformation matrix is 5 to 30;
• and
• the condition number of the actuating transformation matrix is 5 to 30.

An optical arrangement, comprising:

• an optical element unit comprising an optical element;
• and
• an actuating device,
• wherein:
• the actuating device is configured to set in a plurality of R degrees of freedom in each case a situation value which is representative of a relative position or orientation of an element reference of the optical element in relation to a primary reference of the actuating device in the respective degree of freedom;
• the actuating device comprises a plurality of S actuating units, each of which is configured to generate an actuating state at an interface of the actuating unit with respect to the optical element unit;
• the optical element unit and the actuating device define an actuating transformation matrix which is representative of the transformation of the S actuating states into the R situation values;
• a condition number of a transformation matrix is defined by the ratio of the largest singular value of the transformation matrix to the smallest singular value of the transformation matrix;
• and the actuating device and/or the optical element unit is configured in such a way that the condition number of the actuating transformation matrix is 5 to 30.