  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.
