How we can diagnose diphtheria organism in lab?

Cultural Characterisitics of Corynebacterium diphtheriae
Corynebacterium diphtheriae grows well on simple nutrient agar and agar containing blood at the mesophilic temperature range. The growth, however, is not observed on enteric agar formulation and on MacConkey agar.
The growth of C. diphtheriae on agar media is accomplished by growing it on media containing compounds like nalidixic acid and colistin sulfate that are inhibitory to gram-negative bacteria.
Like most corynebacteria, C. diphtheriae also grows well at 37 °C or within the mesophilic temperature range.
Some strains of C. diphtheriae are facultative anaerobes that grow well in a CO2-enriched atmosphere.
The most important culture media used for the isolation of C. diphtheriae is the Sheep Blood Agar (SBA). Other selective media include cystine-tellurite blood agar (CTBA) or freshly prepared Tinsdale medium.
The tellurite present in the medium inhibits the growth of other noncorynebacterium species, but some strains of C. diphtheriae are sensitive to potassium tellurite and require the SBA agar.
For the direct culturing of C. diphtheriae, Tinsdale medium is the best medium, but the medium has a short shelf life.
The identification of C. diphtheriae on Tinsdale medium is efficient in the identification of C. diphtheriae as the bacteria shows both tellurite reductase and cystinase activity.
C. diphtheriae belongs to the Hazard group 2 organisms which might require Containment Level 3 conditions for processing in some cases due to aerosol production.
Growth on serum-based media like Loeffler slants produce colonies with pleomorphic rods, some of which might be club-shaped. The cells might have a beaded appearance due to the terminal reddish-purple polyphosphate granules.