Limits of Modal Insensitivity for Laser Vibrometry, spectral reduction   requires super-symmetry
  Lab measurements showed that identification (ID) and monitoring of objects using remote sensing of their vibration signatures are limited in a couple rare cases. This work provides two necessary conditions to infer that the identification of practical targets to within prescribed bounds; failure to ID the spectrum is shown to be rare. Modal modulation of laser return produces data clusters for adequate spectral ID using slowly swept sine (SSS) and small deflection multi-modal (MM) analyses. Results using these completely different calculations lead to practical removal of a remote sensing concern, spectral "reduction" (SR) of return used for object ID. The optical return provides structural mode ID for non-imaging detection and classification. Calculations using a large spot size to completely paint the vibrating object provide insight for SR found in laboratory measurements which use spot size as a variable. Non-imaging calculations comparing SSS and MM approximations show vibrating rectangular plates have spatially integrated (non-imaging) return that varies substantially among low-frequency vibration modes. The clustering of data from these two methods are the necessary conditions for ID. Theories for SSS and MM describe the signal processing physics for a modal recognition capability and how pure one-dimensional modal targets and super-symmetric square plates can frustrate classification. 
Michael C. Kobold
physics.optics