Did the Sikhs of Punjab wear turban helmets? There is no definitive evidence that conclusively proves that Sikhs ever wore turban helmets. Of the numerous existing 19th century images of Sikhs wearing a helmet, not a single image has ever been found to date showing a Sikh or group of Sikhs wearing a turban helmet.
Without any primary direct evidence, we are only left with secondary circumstantial evidence from the era of the Sikh Kingdom of Maharaja Ranjit Singh that may or may not be references to turban helmets.
Perhaps the best circumstantial evidence comes from a British military journal describing the October 29, 1831 meeting between Maharaja Ranjit Singh and the British Governor General of India, Lord William Bentinck at Ropar on the banks of the Sutlej River:
‘On the following morning, the 29th, the Governor-General went across the Sutlej to witness a review of his Highness's forces, amounting to ten or eleven thousand men. Upon entering the field, a brilliant spectacle presented itself. On the left, an apparently infinite line of cavalry was drawn up, consisting of five thousand ghore-churras dressed in yellow, interspersed at intervals with small bodies of Akalis, dressed in dark blue velved, and high caps surmounted by quoits. On the right were six battalions of infantry, each one thousand strong. Their uniform is a red turban, red coat with black belts and yellow facings, and white trowsers. After these came the horse artillery, consisting of sixteen guns, the greater part brass, but about six of iron. The carriages were slight and the horses very indifferent. Mons. Allard's dragoons, about eight hundred strong, followed these. Their uniform is a steel helmet in the shape of a Sikh turban, red coats with black belts, white trowsers, and jack boots. Their arms, the spear, sword, carbine, and pistols.’ (1832) 
Reference is made to the cavalry troops of the Dragoon regiment under Maharaja Ranjit Singh’s French General Jean Francois Allard as wearing ‘a steel helmet in the shape of a Sikh turban’. No further description of this helmet is given. What type of Sikh turban did this helmet resemble? There were a number of different turban styles worn by Sikhs in the first half of the 19th century and specifically in the 1830’s as can be seen in numerous paintings from that era. Without any further description being provided of the form and functionality of this turban, this account may or may not be a reference to the same style of turban helmet as the few surviving examples from Punjab that we have today. Although it is more than likely that this is a reference to the Punjab turban helmet, at best this account only provides circumstantial evidence in that regard.
In Lord Wilbraham Egerton’s seminal 19th century work on Indian weapons and armour, he provides the following description of the Ghouchara Fauj, a branch of the irregular cavalry of Maharaja Ranjit Singh composed of soldiers from the aristocratic families of Punjab:
‘Some wore a steel helmet inlaid with gold, and surmounted by the “Kalgi” a black heron’s plume. Others wore a cap of steel worked like the cuirass in rings.’ (Egerton, 1880) 
While the former helmet seems to be a reference to the traditional Indo-Persian style of helmet popularly worn by Sikhs of the 19th century, is the latter reference to a ‘cap of steel’ a reference to a Punjab turban helmet? Egerton only provided a partial quote of a earlier source of this description in his book. The full reference that Egerton uses provides more details of this helmet worn by the Ghouchara Fauj. Baron Charles Hugel who visited the Sikh Kingdom of Lahore in 1836 wrote:
‘Some wore a steel helmet, inlaid with gold and surmounted with the kalga or black heron's plume; others wore a cap of steel, worked like the cuirass in rings: this cap lies firmly on the turban, and covers the whole head, having openings for the eyes.’ (Hugel, 1845) 
Hugel’s additional information makes clear that the ‘cap of steel’ that he is referring to and which appears in abbreviated form in Egertons work is an entirely different type of helmet that covers the entire head with only openings for the eyes, clearly not the open face-exposing design of a Punjab turban. The description of the helmet Hugel and Egerton are referring to seems to be similar to 17th century helmets from Sindh that featured a cap like upper part of joined small plates with chain mail falling squarely on the shoulders which covered the whole face with two holes for the eyes (Pant, 1983) 
Although Hugel’s reference to a ‘cap of steel’ describes an entirely different type of helmet and not a Punjab turban helmet, there are other historical references that mention ‘steel caps’.
Lt. William Barr encountered Sikh troops in 1839 while on a military expedition to Peshawar. While visiting the camp of Prince Nau Nihal Singh, Maharaja Ranjit Singhs grandson, Lt. Barr observed troops under Gulab Singh wearing ‘steel caps’.
Our departure was marked by a salute similar to that on our arrival; and though nearly dark, we proceeded to the tents of the Rajah Gholab Singh, whose visit the Colonel was desirous to return. His encampment was situated about three quarters of a mile from the Prince's, and occupied a garden; at one corner of which a party of horsemen, habited in steel caps, exactly like barbers' basins in shape, was drawn up, and presented arms as we passed by. (Barr, 1844) 
Barr’s description of the ‘steel caps’ being shaped like ‘barbers basins’, suggests the shape of a simple singular bowl shaped helmet, as he does not make reference to the distinct top-knot dome shape found on Punjab turban helmets and neither do they resemble a 'barbers basin' in shape. Barr may have been referring to the type of helmet worn by Raja Dhian Singh which had a simple bowl shape without any secondary top-knot dome. Raja Dhian Singh was the brother of Raja Gulab Singh whose cavalry troops Barr encountered wearing these ‘steel caps’.
Sohan Lal Suri, Maharaja Ranjit Singh’s official court chronicler recorded Maharaja Ranjit Singh inspecting a group of Ghorchurra cavalry wearing ‘skull caps’:
On the 17th (28th May 1838 A.D.) 200 horsemen of the Ghorchara Khas stood well-equipped and well-dressed in brocade, with gold and silver saddles and gold-threaded skull caps. The Maharaja inspected them one by one separately and ordered the Raja Kalan to establish them on both sides outside the special portico on the arrival of the glorious Sahibs so that they might feel pleased to see their garments, their horses and their fine armour. 
Suri mentions that the helmets were 'gold-threaded skull caps'. This may be yet another reference to the type of helmet worn by Raja Dhian Singh, Osborne's drawing of which show a string of jewels wrapped around the singular cap-like bowl and likely used to help hold the helmet in place.
It is interesting to note that the term ‘steel cap’ has also been used to describe a more traditional Indo-Persian style helmet as well. Lt. Barr provides the following description of General Allard’s Cuirassiers:
The uniform consisted of a short blue coat and a pair of dark trousers with a narrow red stripe tightly strapped over Wellington boots and spurs. The cuirass was of highly polished steel, or brass, and bore a Gallic cock in the centre of the breast plate. The head-dress was a round steel cap from the apex of which sprung a red horse hair plume. From the cap depended a curtain of chain mail, which hung down over the neck and shoulders. The arms consisted of a flint-lock carbine, and a long steel sword depending from the waist-belt by steel chains. (Barr, 1839) 
The Cuirassiers wore a hemispherical helmet with a singular porte-aigrette plume holder at its apex with a kalgi plume. We have visual evidence of this, as Dr. John Martin Honigberger in his memoirs Thirty-Five Years in the East (London, 1852), provided a drawing of a helmeted Sikh Cuirrassier which exactly matches Barr’s description.
Lt. Colonel Steinbach who spent 9 years in the Lahore army during the time of Maharaja Ranjit Singh and Maharaja Sher Singh writes:
The cavalry wear helmets or steel caps, round which shawls or scarfs are folded. (Steinbach, 1845) 
The arms, which are principally made at Lahore, consist of swords, spears, matchlocks, muskets, pistols, and armour, the latter being composed of helmets or skull-caps, coats of mail, breatplates, gauntlets, and shields. (Steinbach, 1845) 
Steinbach differentiates between ‘helmets’ and what he calls ‘steel caps’ or ‘skull-caps’. It is possible that this cap-like helmet may be a reference to a Punjab turban helmet but without any further details or description this cannot be definitively discerned.
Two other early European references to the Dragoon cavalry regiments of the Sikh cavalry under the command of French General, Jean Francois Allard make references to ‘close-fitting steel helmets’.
The regular cavalry was formed by M. Allard, and is disciplined in the system of the French lancers and dragoons. The uniform of the former is blue with red facings; they are armed with the Polish lance, a light sabre, and pistols. M. Allard represents the men as docile, with excellent qualities for soldiers. The dragoons are a fine body of men, armed with swords, pistols, and long carbines; their clothing is scarlet, with green facings, long jack-boots and buckskins, with black belts, and close-fitting steel helmets. (Asiatic Journal, 1839) 
The Dragoons are fine men, armed with long carbines, pistols and swords. Their appointments are of black leather, with jack boots. Clothing scarlet, with green facings, and close fitting steel helmets, of the Roman pattern. (Oriental Herald, 1838) 
The fact that these helmets are described as ‘close fitting’ in both accounts is an indication that they may be smaller than the traditional Indo-Persian style worn by the overwhelming majority of armored Sikhs during the 19th century. The reference from the Oriental Herald also provides further important details of this helmet and mentions that the ‘close fitting steel helmets’ are ‘of the Roman pattern’.
Although Roman helmets varied in their design and form over the centuries, the Coolus-Mannheim style Roman helmet prevalent during the 1st Century B.C., and worn by Caesar's legions, during his conquest of Gaul  bears the strongest resemblance to the form of a Punjab turban helmet. Military reforms and the need to contain costs during the campaigns of Caesar, led to a progressive simplification of the Roman helmet during this specific time period. The simplified design of the Coolus-Mannheim helmet as a hemispherical bronze cap with minimal decorative elements, lack of cheek-pieces and no neck roll at the back or minimal and without a button or any other ornamental element at its apex at first glance make for a strong resemblance to the shape of a Punjab turban helmet and that is what the author may have been trying to describe when he mentioned its similarity to a Roman helmet.
While most of these European eyewitness accounts refer to General Allards Dragoon regiment of the cavalry as wearing ‘steel caps’, another reference to soldiers wearing ‘steel cap’ helmets can be found in the memoirs of G.T. Vigne who visited the Lahore Kingdom in 1836. While reviewing the troops of Maharaja Ranjit Singh under the command of his other French General, Jean-Baptise Ventura, Vigne observed the following:
We passed down the line of four or five regiments with Runjit, who, from time to time, asked the Baron for his opinion. In the centre was drawn up what is called the Bande-a-casque,—a solid mass of about thirty buglemen, in steel skull-caps, who were blowing with all their might, knowing nothing of music, and making a most horrible din. (Vigne, 1840) 
1. "Meeting Between the Governor-General of India and Runjeet Singh, Lord of the Punjab.", The United Service Journal and Naval and Military Magazine, Part II (London: 1832), 22
2. Wilbraham Egerton, An Illustrated Handbook of Indian Arms (London: 1880), 128
3. Baron Charles Hugel, Travels in Kashmir and the Panjab (London: 1845), 330-331
4. G. N. Pant, Indian Arms and Armour, Volume III (New Delhi: Army Educational Stores, 1983), 39
5. William Barr, Journal of a March from Delhi to Peshawur (London: 1844), 277
6. Sohan Lal Suri, Translator V.S. Suri, Umdat Ut-tawarikh, Daftar III (parts IV-V) (Amritsar: Guru Nanak Dev University, 2002), 152
7. C. Grey, H. L. O. Garrett, European Adventures of Northern India 1785 to 1849 (New Delhi: Asian Educational Services, 1993), 22
8. Lieut. - Colonel Steinbach, The Punjaub ; being a brief Account of the History of the Sikhs (London: 1845), 59
9. Steinbach, 50
10. "The Kingdom of the Sikhs", The Asiatic Journal and Monthly Register, Vol XXVIII (Jan-Apr 1839): 91-92
11. "Runjeet Singh's Army", Parbury's Oriental Herald and Colonial Intelligencer, Vol II (Jul.-Dec. 1838), 575
12. Coolus-Mannheim, http://www.roma-victrix.com/armamentarium/cassides_coolus_mannheim.htm (January, 2013)
13. G. T. Vigne, A Personal Narrative of a Visit to Ghuzni, Kabul, and Afghanistan (London: 1840), 263