  In the standard picture, episodes of luminous quasar activity are directly
related to supermassive black hole (SMBH) growth. The ionising radiation
emitted over a quasar's lifetime alters the ionisation state of the surrounding
intergalactic medium (IGM), enhancing the Ly$\alpha$ forest transmission --
so-called proximity effect -- which can be observed in absorption spectra of
background sources. Owing to the finite speed of light, the transverse
direction of the proximity effect is sensitive to the quasar's radiative
history, resulting in `light echoes' that encode the growth history of the SMBH
on Myr-timescales. In this paper, we introduce a new technique to
photometrically map this quasar light echoes using Ly$\alpha$ forest tomography
by using a carefully selected pair of narrow-band filters. A foreground
narrow-band filter is used to measure Ly$\alpha$ forest transmission along
background galaxies selected as Ly$\alpha$ emitters by a background narrow-band
filter. This novel double narrow-band tomographic technique utilises the higher
throughput and wider field of view of imaging over spectroscopy to efficiently
reconstruct a two-dimensional map of Ly$\alpha$ forest transmission around a
quasar. We present a fully Bayesian framework to measure the luminous quasar
lifetime of a SMBH from photometric IGM tomography, and examine the
observational requirements. This new technique provides an efficient strategy
to map a large area of the sky with a modest observing time and to identify
interesting regions to be examined by further deep 3D follow-up spectroscopic
Ly$\alpha$ forest tomography.
