We report spatially resolved ( FWHM \sim 3.8 - 4.6 ^ { \prime \prime } ) mid-IR imaging observations of the planetary nebula ( PN ) NGC 7027 taken with the 2.5-m telescope aboard the Stratospheric Observatory for Infrared Astronomy ( SOFIA ) . Images of NGC 7027 were acquired at 6.3 , 6.6 , 11.1 , 19.7 , 24.2 , 33.6 , and 37.1 \mu \mathrm { m } using the Faint Object Infrared Camera for the SOFIA Telescope ( FORCAST ) .The observations reveal emission from Polycyclic Aromatic Hydrocarbon ( PAH ) and warm dust ( T _ { D } \sim 90 K ) from the illuminated inner edge of the molecular envelope surrounding the ionized gas and central star . The DustEM code was used to fit the spectral energy distribution of fluxes obtained by FORCAST and the archival infrared spectrum of NGC 7027 acquired by the Short Wavelength Spectrometer ( SWS ) on the Infrared Space Observatory ( ISO ) . Best-fit dust models provide a total dust mass of 5.8 ^ { +2.3 } _ { -2.6 } \times 10 ^ { -3 } \mathrm { M } _ { \odot } , where carbonaceous large ( a = 1.5 \mu m ) and very small ( a \sim 12 \AA ) grains , and PAHs ( 3.1 \AA < a < 12 \AA ) compose 96.5 , 2.2 , and 1.3 \% of the dust by mass , respectively . The 37 \mu m optical depth map shows minima in the dust column density at regions in the envelope that are coincident with a previously identified collimated outflow from the central star . The optical depth minima are also spatially coincident with enhancements in the 6.2 \mu m PAH feature , which is derived from the 6.3 and 6.6 \mu m maps . We interpret the spatial anti-correlation of the dust optical depth and PAH 6.2 \mu m feature strength and their alignment with the outflow from the central star as evidence of dust processing and rapid PAH formation via grain-grain collisions in the post-shock environment of the dense ( n _ { H } \sim 10 ^ { 5 } \mathrm { cm } ^ { -3 } ) photo-dissociation region ( PDR ) and molecular envelope .