Trapping force by a high numerical-aperture microscope objective obeying the sine condition

A commercial high numerical-aperture microscope objective is designed in terms of the sine condition which is needed for two-dimensional space-invariant imaging. The axial trapping efficiency generated by an objective obeying the sine condition is found to be approximately up to 50% smaller than the prediction for an objective obeying the tangent condition which has been currently used in the ray optics theory for trapping force calculations. Our result is in good agreement with the measured value of the trapping efficiency.