PIARC indicates a conversion for opacity measured in [1/m] into [ug/m3] in a 1995 report: "Vehicle Emissions, Air Demand, Environment, Longitudinal Ventilation":

->    1 g = 4,7 m2

However, this may depend on the particle size distribution. It may be applied to particles from vehicle engine emissions.

For transmission/opacity given in %, I found various definitions. A conversion depends on your definition of opacity.

Practically speaking industrial stacks use opacity to monitor particulate emissions on a continuous basis, looking for change to monitor the effectiveness of pollution abatement equipment.  Regulatory jurisdictions typically require actual Source mass emissions measurements at some frequency during the year (EPA methods, Method 5, etc.) usually against some license limit.  The best way to "calibrate" opacity to actual mass emissions is to plot opacity during these actual mass measurements and gradually define the relation.  This works well in steady state, but keep in mind the relation may need further definition outside of that condition.

Thanks Ingo Riess and David Kelly...sounds like quite tricky to get the relationship between opacity and soot mass...but any definition can be use for conversion of opacity in [%] to soot mass in [ug/m3]?

I took the following figures from the aforementioned PIARC 1995 report. As I wrote before, you need to be careful in the application of this conversion. It has been derived for a particular application in road tunnels. Hope, this helps.

In the use of numerical methods (CFD) in Fire Safety Engineering, the mass of smoke (essentially mass of soot) is resolved by solution of differential form of mass transport equation, and then the loss of opacity is estimated with use of models based on this mass density - if you reverse this approach it should fit your problem quite well, as long as we assume the diesel produced soot is similar to one being product of hydrocarbon fires (i think it is a safe assumption).

The main assumption is that the obscuration of light passing through aerosol like smoke follows Lambert-Beer law. To solve this equation, you need to know some constants - from which in your case the most important one will be value of mass extinction coefficient - there is some materials on this, out of which the work of Mullholland in SFPE Handbook of Fire Protection Engineering is msot relevant.

If you wish to learn more about how we apply this in Fire Safety Engineering, you can relate to my paper: https://www.researchgate.net/publication/303686779_Influence_of_Variability_of_Soot_Yield_Parameter_in_assessing_the_safe_conditions_in_Advanced_Modelling_Analysis_Results_of_Physical_and_Numerical_Modelling_Comparison

If you do the reverse-engineering correctly, you should obtain your own value of g/m3 related to [%] loss of opacity, based on mass extinction coefficient related to diesel smoke.

Best regards

Wojciech

Conference Paper Influence of Variability of Soot Yield Parameter in assessin...

Article Experimental correlations for transient soot measurement in ...