  We adapt the Jain--Taylor (2003) shear-ratio geometric lensing method to
measure the dark energy equation of state, and its time derivative from dark
matter haloes in cosmologies with arbitrary spatial curvature. The full
shear-ratio covariance matrix is calculated for lensed sources, including the
intervening large-scale structure and photometric redshift errors as additional
sources of noise, and a maximum likelihood method for applying the test is
presented. Combining with the expected results from the CMB we design an
optimal survey for probing dark energy. A targeted survey imaging 60 of the
largest clusters in a hemisphere with 5-band optical photometric redshifts to a
median galaxy depth of zm=0.9 could measure w0 to a marginal 1-sigma error of
$\Delta$w0=0.5. We marginalize over all other parameters including wa, where
the equation of state is parameterized in terms of scale factor a as
w(a)=w0+wa(1-a). For higher accuracy a large-scale photometric redshift survey
is required. Such a near-future 5-band survey covering 10,000 square degrees to
z_m=0.7 could measure w0 to $\Delta$w0=0.075 and $\Delta$wa=0.33. A stronger
combined constraint is measured at a pivot redshift zp=0.27 of
$\Delta$w(zp)=0.0298. We compare and combine the geometric test with the
cosmological and dark energy parameters measured from planned Baryon Acoustic
Oscillation (BAO) and supernova Type Ia experiments, and find that the
geometric test results combine with a significant reduction in errors due to
different degeneracies. A combination of geometric lensing, CMB and BAO
experiments could achieve a pivot redshift constraint of $\Delta$w(zp)=0.020 at
zp=0.62. Simple relations are presented that show how our lensing results can
be scaled to other telescope classes and survey parameters.
