The range of wavelengths that plants use is called Photosynthetic Active Radiation (PAR). This is measured in units of micro-mol per metre squared per second (umol/m2/s) which is usually called Photosynthetic Photon Flux Density (PPFD).

At midday in mid summer the sun can reach around :-
2000uE = 2000umol/m2/s = 9800FC = 1060W/m2 = 106000LUX.   
Of course, this depends on the latitude where you live.

From the above you might imagine that you could calculate conversion constants between them.  However, this cannot be accurately done.  The trouble with comparing watts/m2, lumens, lux and umol/m2/sec (uEinsteins) is that it is like comparing apples with bananas with pears.  Each system of units refers to different portions of the total light spectrum. So, to produce a set of conversion constants can be somewhat misleading.

The total solar spectrum is measured with a pyranometer in units of watts/m2 relating to light in the 400 to 1100 nanometer wavelength. 

Photosynthetically active radiation (PAR) is measured with a quantum sensor in units of umol/m2/sec  relating to light in the 400 to 700 nanometer wavelength. 

Photometry is measured with a light meter in units of lumens or lux relating to light in the visible 380 to 770 nanometer wavelength. 

In the middle of the day it si possible to arrive at a reasonable equivalence between PAR (PPFD) and Total Energy as measured by a pyranometer.   At mid day the maximum PAR value is about 1800 umol/m2/sec and this relates to about 1000W/m2  or 1000J/m2/sec.  From this you can derive that 1J/m2/sec is roughly equivalent to 1.8 umol/m2/sec.

Settings for solar integrators are often given in J/cm2  or in mol/m2.  The equivalence here is that 100J/cm2 or 1MJ/m2 is equivalent to about 1.8mol/m2.

Typical settings for vine crops in coir or rockwool slabs is abot 0.9MJ/m2, 90J/cm2 or 1.8mol/m2.  This gives an initial setting which must be modified until the run-off EC and quantity meet the recommended guidlines.   Experience may dictate that slightly different settings are required for summer and winter to achieve ideal conditions.

As a matter of interest one mol/m2/sec is equal to Avogadro's number in photons,
6.02  X 10 ²³.

This means that 1 umol/m2/sec relates to 602,200,000,000,000,000 photons reaching the earths surface in each square metre every second.  That an awful lot of photons - maybe keep that number in mind next time you contemplate sunning yourself.

see also solar integration principles