Impact of microscope numerical aperture on microspectrophotometric measurements of hemoglobin in microvessels

In the microspectrophotometric method to measure hemoglobin concentration and oxygen saturation in microvessels it is recommended that a low numerical aperture (NA) condenser be employed to ensure that the recorded image is a true projection of the object. However, this tenet has never been rigorously justified. In this study, the microspectrophotometric method is evaluated using the theory of three-dimensional image formation by a light microscope for a wide range of NA. The results of the calculations show that for measurements for hemoglobin concentration, the recorded image is close to the true projection only when the size of the microvessel is large compared to the degree of smearing ( proportional, variant 1/NA) but small compared to the degree of defocus ( proportional, variant NA(2)). These opposing tendencies lead to an optimum NA for which the errors are minimum. This optimum NA is a function of the size of the microvessel and the manner in which the hemoglobin concentration is distributed within the lumen. For measurements of oxygen saturation, the recorded image is the true projection as long as the measurements are made in regions near the microvessel centerline. For measurements made in regions away from the centerline, good agreement was obtained only when the distribution of oxygen saturation was uniform. Reconstruction of the axisymmetric profiles from the recorded projections showed that the errors in the projections cause the recovered profiles to deviate from the true profiles. These deviations are directly related to the extent by which the recorded projections deviate from the true projection.