The relationship between dust polarization and extinction was determined for the cold dense starless molecular cloud core FeSt 1-457 based on the background star polarimetry of dichroic extinction at near-infrared wavelengths . Owing to the known ( three-dimensional ) magnetic field structure , the observed polarizations from the core were corrected by considering ( a ) the subtraction of the ambient polarization component , ( b ) the depolarization effect of inclined distorted magnetic fields , and ( c ) the magnetic inclination angle of the core . After these corrections , a linear relationship between polarization and extinction was obtained for the core in the range up to A _ { V } \approx 20 mag . The initial polarization vs. extinction diagram changed dramatically after the corrections of ( a ) to ( c ) , with the correlation coefficient being refined from 0.71 to 0.79 . These corrections should affect the theoretical interpretation of the observational data . The slope of the finally obtained polarization–extinction relationship is P _ { H } / E _ { H - K _ { s } } = 11.00 \pm 0.72 \% { mag } ^ { -1 } , which is close to the statistically estimated upper limit of the interstellar polarization efficiency ( Jones 1989 ) . This consistency suggests that the upper limit of interstellar polarization efficiency might be determined by the observational viewing angle toward polarized astronomical objects .