Infrared ellipsometer/polarimeter system, method of calibration, and use thereof

A method of calibrating for nonidealities in mathematical representations of rotated and non-rotated components of a sample system investigating system, which sample system investigating system is sequentially comprised of a source of a beam of electromagnetic wavelengths, a polarizer means, a stage for supporting a sample system, an analyzer means and a detector system, which sample system investigating system is further comprised of at least a first compensator means, said at least a first compensator means being positioned in said sample system investigating system at a location selected from the group consisting of, before and after, said stage for supporting a sample system, and which sample system investigating system optionally comprises a second compensator means positioned in said sample system investigating system at a location complementary to said first compensator means, said position being selected from the group consisting of, respectively, after and before, said stage for supporting said sample system;

• said method comprising the steps of:
• a. empirically obtaining at least two data sets, each of which data sets consists of intensity values measured by said detector system, said intensity values being a function wavelength and of settings of at least two of said sample system investigating system components, which sample system investigating system components are selected from the group consisting of said polarizer means, said analyzer means and present compensator means;
• at least one of which data sets is obtained with said sample system investigating system oriented in a "sample-present" configuration and another of which data sets is obtained with said sample system investigating system oriented in a configuration selected from the group consisting of a "alternative sample-present" and a "straight-through" configuration;
• which "straight-through" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, through said analyzer means and into said detector system;
• and which "sample-present" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, interact with an arbitrary sample system supported by said stage for supporting a sample system, pass through said analyzer means and into said detector system;
• such that in either of said "straight-through" or "sample-present" configurations of said sample system investigating system, said beam of electromagnetic wavelengths is also caused to pass through present compensator means;
• b. applying mathematical formula to said data sets to provide empirically derived numerical values for coefficients of multi-dimensional mathematical series, said dimension of said multi-dimensional mathematical series being determined by the number of sample system investigating system components which were caused to assume various settings during the obtaining of data sets in step a., said sample system investigating system components being selected from the group consisting of said polarizer means, said analyzer means and present compensator means;
• c. effectively deriving analytical non-ideality compensating calibration parameter containing equations for multi-dimensional mathematical series coefficients, each of which analytically derived non-ideality compensating calibration parameter containing equations for multi-dimensional mathematical series coefficients is analogically equivalent to numerical values for corresponding multi-dimensional mathematical series coefficients empirically determined by applying mathematical formula to the data sets as in Step b., said effective analogically equivalent non-ideality compensating calibration parameter containing equations for multi-dimensional mathematical series coefficients being achievable by performing matrix multiplication of non-ideality compensating calibration parameter containing matrices which represent sample system investigating system components and rotation matrices, each thereof being oriented in a series of said sample system investigating system component and rotation matrices to appropriately represent a "straight-through" or a "sample-present" configuration of said sample system investigating system;
• d. performing a simultaneous mathematical regression of Step c., effective analytically arrived at non-ideality compensating calibration parameter containing equations for coefficients of multi-dimensional mathematical series, onto analogically equivalent numerical values for multi-dimensional mathematical series coefficients as arrived at in Step b.;
• such that non-ideality compensating calibration parameters in said effective non-ideality compensating calibration parameter containing equations for multi-dimensional mathematical series coefficients are simultaneously evaluated, based upon an error reducing criteria.

A method of calibrating for nonidealities in mathematical representations of rotated and non-rotated components in a sample system investigating system, which sample system investigating system is sequentially comprised of a source of a beam of electromagnetic wavelengths, a polarizer means, a stage for supporting a sample system, an analyzer means and a detector system, which sample system investigating system is further comprised of at least a first compensator means, said at least a first compensator means being positioned in said sample system investigating system at a location selected from the group consisting of, before and after, said stage for supporting a sample system, and which sample system investigating system optionally comprises a second compensator means positioned in said sample system investigating system at a location complementary to said first compensator means, said position being selected from the group consisting of, respectively, after and before, said stage for supporting said sample system;

• said at least first compensator means in said sample system investigation system being essentially achromatic and of a dual-rhomb construction such that a polarized beam of electromagnetic wavelengths caused to pass therethrough in use, experiences four internal reflections, each of which internal reflections causes a retardance between quadrature components of said polarized beam of electromagnetic wavelengths, selected from the group consisting of one-sixteenth and of three-sixteenths of a wavelength, but which at least first compensator means effects essentially no deviation in the direction of propagation of said beam of electromagnetic wavelengths caused to pass therethrough, even when said at least one compensator means is caused to rotate;
• said method comprising the steps of:
• a. empirically obtaining at least two data sets, each of which data sets consists of intensity values measured by said detector system, said intensity values being a function wavelength and of settings of at least two of said sample system investigating system components, which sample system investigating system components are selected from the group consisting of said polarizer means, said analyzer means and present compensator means;
• at least one of which data sets is obtained with said sample system investigating system oriented in a "sample-present" configuration and another of which data sets is obtained with said sample system investigating system oriented in a configuration selected from the group consisting of "alternative sample-present" and a "straight-through" configuration;
• which "straight-through" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, through said analyzer means and into said detector system;
• and which "sample-present" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, interact with an arbitrary sample system supported by said stage for supporting a sample system, pass through said analyzer means and into said detector system;
• such that in either of said "straight-through" or "sample-present" configurations of said sample system investigating system, said beam of electromagnetic wavelengths is also caused to pass through present compensator means;
• b. applying mathematical formula to said data sets to provide empirically derived numerical values for coefficients of multi-dimensional mathematical series, said dimension of said multi-dimensional mathematical series being determined by the number of sample system investigating system components which were caused to assume various azimuthal angle settings during the obtaining of data sets in step a., said sample system investigating system components, the azimuthal angles of which were variously set during acquisition of said data sets, being selected from the group consisting of said polarizer means, said analyzer means and present compensator means;
• c. effectively deriving analytical non-ideality compensating calibration parameter containing equations for multi-dimensional mathematical series coefficients, each of which effective analytically derived non-ideality compensating calibration parameter containing equations for multi-dimensional mathematical series coefficients is analogically equivalent to numerical values for corresponding multi-dimensional mathematical series coefficients empirically determined by applying mathematical formula to the data sets as in Step b., said analogically equivalent non-ideality compensating calibration parameter containing equations for multi-dimensional mathematical series coefficients being achievable by performing matrix multiplication of non-ideality compensating calibration parameter containing matrices which represent sample system investigating system components and rotation matrices, each thereof being oriented in a series of said sample system investigating system component and rotation matrices to appropriately represent a "straight-through" or a "sample-present" configuration of said sample system investigating system;
• d. performing a simultaneous mathematical regression of Step c., analytically arrived at effective non-ideality compensating calibration parameter containing equations for coefficients of multi-dimensional mathematical series, onto analogically equivalent numerical value for multi-dimensional mathematical series coefficients as arrived at in Step b.;
• such that non-ideality compensating calibration parameters in said effective non-ideality compensating calibration parameter containing equations for a multi-dimensional mathematical series coefficients are simultaneously evaluated, based upon an error reducing criteria.

A method of calibrating for nonidealities in mathematical representations of rotated and nonrotated components of a sample system investigating system, which sample system investigating system is sequentially comprised of a source of a beam of electromagnetic wavelengths, a polarizer means, a stage for supporting a sample system, an analyzer means and a detector system, which sample system investigating system is further comprised of at least a first compensator means, said at least a first compensator means being positioned in said sample system investigating system at a location selected from the group consisting of, before and after, said stage for supporting a sample system, and which sample system investigating system optionally comprises a second compensator means positioned in said sample system investigating system at a location complementary to said first compensator means, said position being selected from the group consisting of, respectively, after and before, said stage for supporting said sample system;

• said method comprising the steps of:
• a. empirically obtaining at least two data sets, each of which data sets consists of intensity values measured by said detector system, said intensity values being a function of wavelength and of rotated settings of azimuthal angles of said analyzer means and said polarizer means of said sample system investigating system;
• one of which data sets is obtained with said sample system investigating system oriented in a "sample-present" configuration such that in one case a compensator means is present and in the other case a present compensator means is not present;
• which "sample-present" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, interact with an arbitrary sample system supported by said stage for supporting a sample system, pass through said analyzer means and into said detector system;
• such that said beam of electromagnetic wavelengths is also caused to pass through any present compensator means;
• b. applying mathematical formula to said data sets to provide empirically derived numerical values for coefficients of two-dimensional mathematical series, said dimension of said two-dimensional mathematical series being determined by the number of sample system investigating system components, namely the analyzer means and the polarizer means, which were caused to assume various azimuthal angle settings during the obtaining of data sets in step a.;
• c. effectively deriving analytical non-ideality compensating calibration parameter containing equations for two-dimensional mathematical series coefficients, each of which effective analytically derived non-ideality compensating calibration parameter containing equations for two-dimensional mathematical series coefficients is analogically equivalent to numerical values for corresponding two-dimensional mathematical series coefficients empirically determined by applying mathematical formula to the data sets as in Step b., said analogically equivalent non-ideality compensating calibration parameter containing equations for two-dimensional mathematical series coefficients being achievable by performing matrix multiplication of non-ideality compensating calibration parameter containing matrices which represent sample system investigating system components and rotation matrices, each thereof being oriented in a series of said sample system investigating system component and rotation matrices to appropriately represent a "straight-through" or a "sample-present" configuration of said sample system investigating system;
• d. performing a simultaneous mathematical regression of Step c., analytically arrived at effective non-ideality compensating calibration parameter containing equations for coefficients of two-dimensional mathematical series, onto analogically equivalent numerical value for two-dimensional mathematical series coefficients as arrived at in Step b.;
• such that non-ideality compensating calibration parameters in said effective non-ideality compensating calibration parameter containing equations for two-dimensional mathematical series coefficients are simultaneously evaluated, based upon an error reducing criteria.

A method of calibrating for nonidealities in mathematical representations of rotated and non-rotated components of a sample system investigating system, which sample system investigating system is sequentially comprised of a source of a beam of electromagnetic wavelengths, a polarizer means, a stage for supporting a sample system, an analyzer means and a detector system, which sample system investigating system is further comprised of at least a first compensator means, said at least a first compensator means being positioned in said sample system investigating system at a location selected from the group consisting of, before and after, said stage for supporting a sample system, and which sample system investigating system optionally comprises a second compensator means positioned in said sample system investigating system at a location complementary to said first compensator means, said position being selected from the group consisting of, respectively, after and before, said stage for supporting said sample system;

• said method comprising the steps of:
• a. empirically obtaining at least three data sets, each of which data sets consists of intensity values measured by said detector system, said intensity values being a function of wavelength and of rotated settings of azimuthal angles of said analyzer means and said polarizer means of said sample system investigating system;
• one of which data sets is obtained with said sample system investigating system oriented in a configuration selected from the group consisting of a "sample-present" and a "straight-through" configuration;
• a second of which data sets is obtained with said sample system investigating system oriented in an "alternative sample-present" configuration;
• and a third of which data sets is obtained with said sample system investigating system oriented in a configuration selected from the group consisting of, (wherein a present compensator means is removed, and wherein an "alternative sample-system" is substituted for a previously present sample-system);
• which "straight-through" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, through said analyzer means and into said detector system;
• and which "sample-present" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, interact with an arbitrary sample system supported by said stage for supporting a sample system, pass through said analyzer means and into said detector system;
• such that in either of said "straight-through" or "sample-present" configurations of said sample system investigating system, said beam of electromagnetic wavelengths is also caused to pass through any present compensator means;
• b. applying mathematical formula to said data sets to provide empirically derived numerical values for coefficients of two-dimensional mathematical series, said dimension of said two-dimensional mathematical series being determined by the number of sample system investigating system components, namely the analyzer means and the polarizer means, which were Caused to assume various azimuthal angle settings during the obtaining of data sets in step a.;
• c. effectively deriving analytical non-ideality compensating calibration parameter containing equations for two-dimensional mathematical series coefficients, each of which effective analytically derived non-ideality compensating calibration parameter containing equations for two-dimensional mathematical series coefficients is analogically equivalent to numerical values for corresponding two-dimensional mathematical series coefficients empirically determined by applying mathematical formula to the data sets as in Step b., said analogically equivalent non-ideality compensating calibration parameter containing equations for two-dimensional mathematical series coefficients being achievable by performing matrix multiplication of non-ideality compensating calibration parameter containing matrices which represent sample system investigating system components and rotation matrices, each thereof being oriented in a series of said sample system investigating system component and rotation matrices to appropriately represent a "straight-through" or a "sample-present" configuration of said sample system investigating system;
• d. performing a simultaneous mathematical regression of Step c., analytically arrived at effective non-ideality compensating calibration parameter containing equations for coefficients of two-dimensional mathematical series, onto analogically equivalent numerical value for two-dimensional mathematical series coefficients as arrived at in Step b.;
• such that non-ideality compensating calibration parameters in said effective non-ideality compensating calibration parameter containing equations for two-dimensional mathematical series coefficients are simultaneously evaluated, based upon an error reducing criteria.

A method of calibrating for nonidealities in mathematical representations of rotated and non-rotated components of a sample system investigating system, which sample system investigating system is sequentially comprised of a source of a beam of electromagnetic wavelengths, a polarizer means, a stage for supporting a sample system, an analyzer means and a detector system, which sample system investigating system is further comprised of at least a first compensator means, said at least a first compensator means being positioned in said sample system investigating system at a location selected from the group consisting of, before and after, said stage for supporting a sample system, and which sample system investigating system optionally comprises a second compensator means positioned in said sample system investigating system at a location complementary to said first compensator means, said position being selected from the group consisting of, respectively, after and before, said stage for supporting said sample system;

• said method comprising the steps of:
• a. empirically obtaining at least two data sets, each of which data sets consists of intensity values measured by said detector system, said intensity values being a function of wavelength and of rotated settings of azimuthal angles of a component selected from the group consisting of (said polarizer means and said analyzer means), and one said compensator means of said sample system investigating system;
• one of which data sets is obtained with said sample system investigating system oriented in a "sample-present" configuration, and one of which data is obtained with said sample system investigating system oriented in a configuration selected from the group consisting of "alternative sample-present" and "straight-through";
• which "straight-through" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, through said analyzer means and into said detector system;
• and which "sample-present" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, interact with an arbitrary sample system supported by said stage for supporting a sample system, pass through said analyzer means and into said detector system;
• such that in either of said "straight-through" or "sample-present" configurations of said sample system investigating system, said beam of electromagnetic wavelengths is also caused to pass through present compensator means;
• b. applying mathematical formula to said data sets to provide empirically derived numerical values for coefficients of two-dimensional mathematical series, said dimension of said two-dimensional mathematical series being determined by the number of sample system investigating system components, namely the polarizer means and compensator means, which were caused to assume various azimuthal angle settings during the obtaining of data sets in step a.;
• c. effectively deriving analytical non-ideality compensating calibration parameter containing equations for two-dimensional mathematical series coefficients, each of which effective analytically derived non-ideality compensation calibration parameter containing equations for two-dimensional mathematical series coefficients is analogically equivalent to numerical values for corresponding two-dimensional mathematical series coefficients empirically determined by applying mathematical formula to the data sets as in Step b., said analogically equivalent non-ideality compensating calibration parameter containing equations for two-dimensional mathematical series coefficients being achievable by performing matrix multiplication of non-ideality compensating calibration parameter containing matrices which represent sample system investigating system components and rotation matrices, each thereof being oriented in a series of said sample system investigating system component and rotation matrices to appropriately represent a "straight-through" or a "sample-present" configuration of said sample system investigating system;
• d. performing a simultaneous mathematical regression of Step c., analytically arrived at effective non-ideality compensating calibration parameter containing equations for coefficients of two-dimensional mathematical series, onto analogically equivalent numerical value for two-dimensional mathematical series coefficients as arrived at in Step b.;
• such that non-ideality compensating calibration parameters in said effective non-ideality compensating calibration parameter containing equations for two-dimensional mathematical series coefficients are simultaneously evaluated, based upon an error reducing criteria.

A method of calibrating for nonidealities in mathematical representations of rotated and non-rotated components of a sample system investigating system, which sample system investigating system is sequentially comprised of a source of a beam of electromagnetic wavelengths, a polarizer means, a stage for supporting a sample system, an analyzer means and a detector system, which sample system investigating system is further comprised of a first compensator means, said first compensator means being positioned in said sample system investigating system at a location selected from the group consisting of, before and after, said stage for supporting a sample system, and which sample system investigating system further comprises a second compensator means positioned in said sample system investigating system at a location complementary to said first compensator means, said position being selected from the group consisting of, respectively, after and before, said stage for supporting said sample system;

• said method comprising the steps of:
• a. empirically obtaining at least two data sets, each of which data sets consists of intensity values measured by said detector system, said intensity values being a function of wavelength and of rotated settings of azimuthal angles of said first compensator means and said second compensator means of said sample system investigating system;
• one of which data sets is obtained with said sample system investigating system oriented in a "sample-present" configuration, and one of which data is obtained with said sample system investigating system oriented in a configuration selected from the group consisting of "alternative sample-present" and "straight-through";
• which "straight-through" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, through said analyzer means and into said detector system;
• and which "sample-present" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, interact with an arbitrary sample system supported by said stage for supporting a sample system, pass through said analyzer means and into said detector system;
• such that in either of said "straight-through" or "sample-present" configurations of said sample system investigating system, said beam of electromagnetic wavelengths is also caused to pass through present first and second compensator means;
• b. applying mathematical formula to said data sets to provide empirically derived numerical values for coefficients of two-dimensional mathematical series, said dimension of said two-dimensional mathematical series being determined by the number of sample system investigating system components, namely the first compensator means and the second compensator means, which were caused to assume various rotated azimuthal angle settings during the obtaining of data sets in step a.;
• c. effectively deriving analytical non-ideality compensating calibration parameter containing equations for two-dimensional mathematical series coefficients, each of which effective analytically derived non-ideality compensating calibration parameter containing equations for two-dimensional mathematical series coefficients is analogically equivalent to numerical values for corresponding two-dimensional mathematical series coefficients empirically determined by applying mathematical formula to the data sets as in Step b., said analogically equivalent non-ideality compensating calibration parameter containing equations for two-dimensional mathematical series coefficients being achievable by performing matrix multiplication of non-ideality compensating calibration parameter containing matrices which represent sample system investigating system components and rotation matrices, each thereof being oriented in a series of said sample system investigating system component and rotation matrices to appropriately represent a "straight-through" or a "sample-present" configuration of said sample system investigating system;
• d. performing a simultaneous mathematical regression of Step c., analytically arrived at effective non-ideality compensating calibration parameter containing equations for coefficients of two-dimensional mathematical coefficients, onto analogically equivalent numerical value for two-dimensional mathematical series coefficients as arrived at in Step b.;
• such that non-ideality compensating calibration parameters in said effective non-ideality compensating calibration parameter containing equations for two-dimensional mathematical series coefficients are simultaneously evaluated, based upon an error reducing criteria.

A method of calibrating for nonidealities in mathematical representations of rotated and non-rotated components of a sample system investigating system, which sample system investigating system is sequentially comprised of a source of a beam of electromagnetic wavelengths, a polarizer means, a stage for supporting a sample system, an analyzer means and a detector system, which sample system investigating system is further comprised of at least a first compensator means, said at least a first compensator means being positioned in said sample system investigating system at a location selected from the group consisting of, before and after, said stage for supporting a sample system, and which sample system investigating system optionally comprises a second compensator means positioned in said sample system investigating system at a location complementary to said first compensator means, said position being selected from the group consisting of, respectively, after and before, said stage for supporting said sample system;

• said method comprising the steps of:
• a. empirically obtaining intensity value data sets measured by said detector system, said intensity value data sets being a function of wavelength and of settings of at least two of said sample system investigating system components, which sample system investigating system components are selected from the group consisting of said polarizer means, said analyzer means and present compensator means;
• at least one of which intensity value data sets is obtained with said sample system investigating system oriented in a "sample-present" configuration and at least one of which data sets is obtained with said sample system investigating system oriented in a configuration selected from the group consisting of "alternative sample-present" and "straight-through";
• which "straight-through" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, through said analyzer means and into said detector system;
• and which "sample-present" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, interact with an arbitrary sample system supported by said stage for supporting a sample system, pass through said analyzer means and into said detector system;
• such that in either of said "straight-through" or "sample-present" configurations of said sample system investigating system, said beam of electromagnetic wavelengths is also caused to pass through present compensator means;
• b. effectively deriving analytical non-ideality compensating calibration parameter containing intensity equations for said sample system investigating system which correspond to said empirically obtained intensities, said effective analytically derived non-ideality compensating calibration parameter containing intensity equations being achievable by multiplying calibration parameter containing matrix representations of each sample system investigating system component, and rotation matrices, in a sample system investigating system representing sequence;
• and
• c. performing a simultaneous mathematical regression of empirically obtained intensity values onto effective analogically equivalent analytically derived calibration parameter containing equations obtained in steps a. and b;
• such that non-ideality compensating calibration parameters in said non-ideality compensating calibration parameter containing effective analytically derived equations are simultaneously evaluated, based upon an error reducing criteria.

A method of calibrating for nonidealities in mathematical representations of rotated and non-rotated components of a sample system investigating system, which sample system investigating system is sequentially comprised of a source of a beam of electromagnetic wavelengths, a polarizer means, a stage for supporting a sample system, an analyzer means for selecting a state of polarization in said beam of electromagnetic wavelengths and a detector system, which sample system investigating system is further comprised of at least a first compensator means, said at least a first compensator means being positioned in said sample system investigating system at a location selected from the group consisting of, before and after, said stage for supporting a sample system, and which sample system investigating system optionally comprises a second compensator means positioned in said sample system investigating system at a location complementary to said first compensator means, said position being selected from the group consisting of, respectively, after and before, said stage for supporting said sample system;

• said at least first compensator means in said sample system investigation system being essentially achromatic and of a dual-rhomb construction such that a polarized beam of electromagnetic wavelengths caused to pass therethrough in use, experiences four internal reflections, each of which internal reflections causes a retardance between quadrature components of said polarized beam of electromagnetic wavelengths, selected from the group consisting of one-sixteenth and of three-sixteenths of a wavelength, but which at least first compensator means effects essentially no deviation in the direction of propagation of said beam of electromagnetic wavelengths caused to pass therethrough, even when said at least one compensator means is caused to rotate;
• said method comprising the steps of:
• a. empirically obtaining intensity value data sets measured by said detector system, said intensity value data sets being a function of wavelength and of rotated settings of azimuthal angles of at least two of said sample system investigating system components, which sample system investigating system components are selected from the group consisting of said polarizer means, said analyzer means and present compensator means;
• at least one of which intensity value data sets is obtained with said sample system investigating system oriented in a "sample-present" configuration and at least one of which data sets is obtained with said sample system investigating system oriented in a configuration selected from the group consisting of a "alternative sample-present" and a "straight-through" configuration;
• which "straight-through" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, through said analyzer means and into said detector system;
• and which "sample-present" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, interact with an arbitrary sample system supported by said stage for supporting a sample system, pass through said analyzer means and into said detector system;
• such that in either of said "straight-through" or "sample present" configurations of said sample system investigating system, said beam of electromagnetic wavelengths is also caused to pass through present compensator means;
• b. effectively deriving analytical non-ideality compensating calibration parameter containing intensity equations for said sample system investigating system which correspond to said empirically obtained intensities, said effective analytically derived non-ideality compensating calibration parameter containing intensity equations being achievable by multiplying calibration parameter containing matrix representations of each sample system investigating system component, and rotation matrices, in a sample system investigating system representing sequence;
• and
• c. performing a simultaneous mathematical regression of empirically obtained intensity values onto effective analogically equivalent analytically derived calibration parameter containing equations obtained in steps a. and b;
• such that non-ideality compensating calibration parameters in said effective non-ideality compensating calibration parameter containing analytically derived equations are simultaneously evaluated, based upon an error reducing criteria.

A method of calibrating for nonidealities in mathematical representations of rotated and nonrotated components of a sample system investigating system, which sample system investigating system is sequentially comprised of a source of a beam of electromagnetic wavelengths, a polarizer means, a stage for supporting a sample system, an analyzer means and a detector system, which sample system investigating system is further comprised of at least a first compensator means, said at least a first compensator means being positioned in said sample system investigating system at a location selected from the group consisting of, before and after, said stage for supporting a sample system, and which sample system investigating system optionally comprises a second compensator means positioned in said sample system investigating system at a location complementary to said first compensator means, said position being selected from the group consisting of, respectively, after and before, said stage for supporting said sample system;

• said method comprising the steps of:
• a. empirically obtaining at least two data sets, each of which data sets consists of intensity values measured by said detector system, said intensity values being a function of wavelength and of rotated settings of azimuthal angles of said analyzer means and said polarizer means of said sample system investigating system;
• one of which data sets is obtained with said sample system investigating system oriented in a "sample-present" configuration such that in one case a compensator means is present and in the other case a present compensator means is not present;
• which "sample-present" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, interact with an arbitrary sample system supported by said stage for supporting a sample system, pass through said analyzer means and into said detector system;
• such that said beam of electromagnetic wavelengths is also caused to pass through any present compensator means;
• b. effectively deriving analytical non-ideality compensating calibration parameter containing intensity equations for said sample system investigating system which correspond to said empirically obtained intensities, said effective analytically derived non-ideality compensating calibration parameter containing intensity equations being achievable by multiplying calibration parameter containing matrix representations of each sample system investigating system component, and rotation matrices, in a sample system investigating system representing sequence;
• and
• c. performing a simultaneous mathematical regression of empirically obtained intensity values onto effective analogically equivalent analytically derived calibration parameter containing equations obtained in steps a. and b;
• such that non-ideality compensating calibration parameter in said effective non-ideality compensating calibration parameter containing equations are simultaneously evaluated, based upon an error reducing criteria.

A method of calibrating for nonidealities in mathematical representations of rotated and non-rotated components of a sample system investigating system, which sample system investigating system is sequentially comprised of a source of a beam of electromagnetic wavelengths, a polarizer means, a stage for supporting a sample system, an analyzer means and a detector system, which sample system investigating system is further comprised of at least a first compensator means, said at least a first compensator means being positioned in said sample system investigating system at a location selected from the group consisting of, before and after, said stage for supporting a sample system, and which sample system investigating system optionally comprises a second compensator means positioned in said sample system investigating system at a location complementary to said first compensator means, said position being selected from the group consisting of, respectively, after and before, said stage for supporting said sample system;

• said method comprising the steps of:
• a. empirically obtaining at least three data sets, each of which data sets consists of intensity values measured by said detector system, said intensity values being a function of wavelength and of rotated settings of azimuthal angles of said analyzer means and said polarizer means of said sample system investigating system;
• one of which data sets is obtained with said sample system investigating system oriented in a configuration selected from the group consisting of a "sample-present" and a "straight-through" configuration;
• a second of which data sets is obtained with said sample system investigating system oriented in an "alternative sample-present" configuration;
• and a third of which data sets is obtained with said sample system investigating system oriented in a configuration selected from the group consisting of, (wherein a present compensator means is removed, and wherein an "alternative sample-system" is substituted for a previously present "sample-system");
• which "straight-through" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, through said analyzer means and into said detector system;
• and which "sample-present" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, interact with an arbitrary sample system supported by said stage for supporting a sample system, pass through said analyzer means and into said detector system;
• such that in either of said "straight-through" or "sample-present" configurations of said sample system investigating system, said beam of electromagnetic wavelengths is also caused to pass through any present compensator means;
• b. effectively deriving analytical non-ideality compensating calibration parameter containing intensity equations for said sample system investigating system which correspond to said empirically obtained intensities, said effective analytically derived non-ideality compensating calibration parameter containing intensity equations being achievable by multiplying calibration parameter containing matrix representations of each sample system investigating system component, and rotation matrices, in a sample system investigating system representing sequence;
• and
• c. performing a simultaneous mathematical regression of empirically obtained intensity values onto effective analogically equivalent analytically derived calibration parameter containing equations obtained in steps a. and b;
• such that non-ideality compensating calibration parameters in said effective non-ideality compensating calibration parameter containing equations are simultaneously evaluated, based upon an error reducing criteria.

A method of calibrating for nonidealities in mathematical representations of rotated and non-rotated components of a sample system investigating system, which sample system investigating system is sequentially comprised of a source of a beam of electromagnetic wavelengths, a polarizer means, a stage for supporting a sample system, an analyzer means and a detector system, which sample system investigating system is further comprised of at least a first compensator means, said at least a first compensator means being positioned in said sample system investigating system at a location selected from the group consisting of, before and after, said stage for supporting a sample system, and which sample system investigating system optionally comprises a second compensator means positioned in said sample system investigating system at a location complementary to said first compensator means, said position being selected from the group consisting of, respectively, after and before, said stage for supporting said sample system;

• said method comprising the steps of:
• a. empirically obtaining at least two data sets, each of which data sets consists of intensity values measured-by said detector system, said intensity values being a function of wavelength and of rotated settings of azimuthal angles of a component selected from the group consisting of (said polarizer means and said analyzer means), and one said compensator means of said sample system investigating system;
• one of which data sets is obtained with said sample system investigating system oriented in a "sample-present" configuration, and one of which data is obtained with said sample system investigating system oriented in a configuration selected from the group consisting of "alternative sample-present" and "straight-through";
• which "straight-through" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, through said analyzer means and into said detector system;
• and which "sample-present" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, interact with an arbitrary sample system supported by said stage for supporting a sample system, pass through said analyzer means and into said detector system;
• such that in either of said "straight-through" or "sample-present" configurations of said sample system investigating system, said beam of electromagnetic wavelengths is also caused to pass through present compensator means;
• b. effectively deriving analytical non-ideality compensating calibration parameter containing intensity equations for said sample system investigating system which correspond to said empirically obtained intensities, said effective analytically derived non-ideality compensating calibration parameter containing intensity equations being achievable by multiplying calibration parameter containing matrix representations of each sample system investigating system component, and rotation matrices, in a sample system investigating system representing sequence;
• and
• c. performing a simultaneous mathematical regression of empirically obtained intensity values onto effective analogically equivalent analytically derived calibration parameter containing equations obtained in steps a. and b;
• such that non-ideality compensating calibration parameters in said effective non-ideality compensating calibration parameter containing equations are simultaneously evaluated, based upon an error reducing criteria.

A method of calibrating for nonidealities in mathematical representations of rotated and non-rotated components of a sample system investigating system, which sample system investigating system is sequentially comprised of a source of a beam of electromagnetic wavelengths, a polarizer means, a stage for supporting a sample system, an analyzer means and a detector system, which sample system investigating system is further comprised of a first compensator means, said first compensator means being positioned in said sample system investigating system at a location selected from the group consisting of, before and after, said stage for supporting a sample system, and which sample system investigating system further comprises a second compensator means positioned in said sample system investigating system at a location complementary to said first compensator means, said position being selected from the group consisting of, respectively, after and before, said stage for supporting said sample system;

• said method comprising the steps of:
• a. empirically obtaining at least two data sets, each of which data sets consists of intensity values measured by said detector system, said intensity values being a function of wavelength and of rotated settings of azimuthal angles of said first compensator means and said second compensator means of said sample system investigating system;
• one of which data sets is obtained with said sample system investigating system oriented in a "sample-present" configuration, and one of which data is obtained with said sample system investigating system oriented in a configuration selected from the group consisting of "alternative sample-present" and "straight-through";
• which "straight-through" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, through said analyzer means and into said detector system;
• and which "sample-present" configuration results from orienting said sample system investigating system such that a beam of electromagnetic wavelengths provided by said source of a beam of electromagnetic wavelengths is caused to pass through said polarization means, interact with an arbitrary sample system supported by said stage for supporting a sample system, pass through said analyzer means and into said detector system;
• such that in either of said "straight-through" or "sample-present" configurations of said sample system investigating system, said beam of electromagnetic wavelengths is also caused to pass through present first and second compensator means;
• b. effectively deriving analytical non-ideality compensating calibration parameter containing intensity equations for said sample system investigating system which correspond to said empirically obtained intensities, said effective analytically derived non-ideality compensating calibration parameter containing intensity equations being achievable by multiplying calibration parameter containing matrix representations of each sample system investigating system component, and rotation matrices, in a sample system investigating system representing sequence;
• and
• c. performing a simultaneous mathematical regression of empirically obtained intensity values onto effective analogically equivalent analytically derived calibration parameter containing equations obtained in steps a. and b;
• such that non-ideality compensating calibration parameters in said effective non-ideality compensating calibration parameter containing equations are simultaneously evaluated, based upon an error reducing criteria.