A method of measuring an absorption spectrum of nanoscale objects, comprising: a) rastering a nanoscale object under a scanning probe tip of a scanning atomic force microscope; b) illuminating said nanoscale object and said scanning probe tip with a frequency tunable coherent light source along a sample arm of an interferometer; c) combining a scattered coherent light beam from said nanoscale object and said scanning probe tip along said sample arm with a beam of light from said frequency tunable light source reflected from a position adjustable reflector in a reference arm of the interferometer and directing the combined coherent light beams into a detector; d) demodulating an output signal from said detector to give second or higher harmonic demodulation signals and, using the second or higher harmonic demodulation signals, adjusting a position of the position adjustable reflector to give an optical phase difference between said light beams in said reference arm and said sample arm to be in a range from about 0.4π to about 0.6π, or from about -0.4π to about -0.6π, and maintaining said position using feedback to maintain the optical path difference; e) obtaining π/2 optical phase difference by minimization of second or higher harmonic demodulation signals with adjustment of the position of the position adjustable reflector when the scanning probe tip is on a sample location containing no resonances or on a metal substrate; and f) obtaining an image of signal intensity being proportional to the imaginary part of infrared absorption coefficient of the sample through the combination of scanning probe microscopy and light scattering from a sharp scanning probe tip with said procedure of setting specific homodyne phase in the interferometer. a) rastering a nanoscale object under a scanning probe tip of a scanning atomic force microscope; b) illuminating said nanoscale object and said scanning probe tip with a frequency tunable coherent light source along a sample arm of an interferometer; c) combining a scattered coherent light beam from said nanoscale object and said scanning probe tip along said sample arm with a beam of light from said frequency tunable light source reflected from a position adjustable reflector in a reference arm of the interferometer and directing the combined coherent light beams into a detector; d) demodulating an output signal from said detector to give second or higher harmonic demodulation signals and, using the second or higher harmonic demodulation signals, adjusting a position of the position adjustable reflector to give an optical phase difference between said light beams in said reference arm and said sample arm to be in a range from about 0.4π to about 0.6π, or from about -0.4π to about -0.6π, and maintaining said position using feedback to maintain the optical path difference; e) obtaining π/2 optical phase difference by minimization of second or higher harmonic demodulation signals with adjustment of the position of the position adjustable reflector when the scanning probe tip is on a sample location containing no resonances or on a metal substrate; and f) obtaining an image of signal intensity being proportional to the imaginary part of infrared absorption coefficient of the sample through the combination of scanning probe microscopy and light scattering from a sharp scanning probe tip with said procedure of setting specific homodyne phase in the interferometer.